Relevant bibliographies by topics / Schauder estimate

Academic literature on the topic 'Schauder estimate'

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Published: 9 March 2023
Last updated: 10 March 2023

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Journal articles on the topic "Schauder estimate"

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Du, Kai, and Jiakun Liu. "A Schauder estimate for stochastic PDEs." Comptes Rendus Mathematique 354, no. 4 (April 2016): 371–75. http://dx.doi.org/10.1016/j.crma.2016.01.010.

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Imbert, Cyril, and Luis Silvestre. "The Schauder estimate for kinetic integral equations." Analysis & PDE 14, no. 1 (February 19, 2021): 171–204. http://dx.doi.org/10.2140/apde.2021.14.171.

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Nardi, Giacomo. "Schauder estimate for solutions of Poisson’s equation with Neumann boundary condition." L’Enseignement Mathématique 60, no. 3 (2014): 421–35. http://dx.doi.org/10.4171/lem/60-3/4-9.

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Liu, Xiangao, Zixuan Liu, and Kui Wang. "Interior estimates of harmonic heat flow." International Journal of Mathematics 32, no. 07 (March 31, 2021): 2150039. http://dx.doi.org/10.1142/s0129167x21500397.

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Motivated by Giaquinta and Hildebrandt’s regularity result for harmonic mappings [M. Giaquinta and S. Hildebrandt, A priori estimates for harmonic mappings, J. Reine Angew. Math. 1982(336) (1982) 124–164, Theorems 3 and 4], we show a [Formula: see text]-regularity result of the harmonic flow between two Riemannian manifolds when the image is in a regular geodesic ball. The proof is based on De Giorgi–Moser’s iteration and Schauder estimate.
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Luo, Yousong, and Neil S. Trudinger. "Linear second order elliptic equations with Venttsel boundary conditions." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 118, no. 3-4 (1991): 193–207. http://dx.doi.org/10.1017/s0308210500029048.

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SynopsisWe prove a Schauder estimate for solutions of linear second order elliptic equations with linear Venttsel boundary conditions, and establish an existence result for classical solutions for such boundary value problems.
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Liang, Xiao, Linshan Wang, and Ruili Wang. "Random Attractor of Reaction-Diffusion Hopfield Neural Networks Driven by Wiener Processes." Mathematical Problems in Engineering 2018 (2018): 1–11. http://dx.doi.org/10.1155/2018/2538658.

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This paper studies the global existence and uniqueness of the mild solution for reaction-diffusion Hopfield neural networks (RDHNNs) driven by Wiener processes by applying a Schauder fixed point theorem and a priori estimate; then the random attractor for this system is also studied by constructing proper random dynamical system.
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Imbert, Cyril, and Clément Mouhot. "The Schauder estimate in kinetic theory with application to a toy nonlinear model." Annales Henri Lebesgue 4 (May 27, 2021): 369–405. http://dx.doi.org/10.5802/ahl.75.

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Juodagalvytė, Rita, Grigory Panasenko, and Konstantinas Pileckas. "Steady-State Navier–Stokes Equations in Thin Tube Structure with the Bernoulli Pressure Inflow Boundary Conditions: Asymptotic Analysis." Mathematics 9, no. 19 (September 30, 2021): 2433. http://dx.doi.org/10.3390/math9192433.

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Steady-state Navier–Stokes equations in a thin tube structure with the Bernoulli pressure inflow–outflow boundary conditions and no-slip boundary conditions at the lateral boundary are considered. Applying the Leray–Schauder fixed point theorem, we prove the existence and uniqueness of a weak solution. An asymptotic approximation of a weak solution is constructed and justified by an error estimate.
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FELLI, VERONICA, and MATTHIAS SCHNEIDER. "COMPACTNESS AND EXISTENCE RESULTS FOR DEGENERATE CRITICAL ELLIPTIC EQUATIONS." Communications in Contemporary Mathematics 07, no. 01 (February 2005): 37–73. http://dx.doi.org/10.1142/s0219199705001623.

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This paper is devoted to the study of degenerate critical elliptic equations of Caffarelli–Kohn–Nirenberg type. By means of blow-up analysis techniques, we prove an a priori estimate in a weighted space of continuous functions. From this compactness result, the existence of a solution to our problem is proved by exploiting the homotopy invariance of the Leray–Schauder degree.
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Chen, Wenxiong, Congming Li, and Yan Li. "A direct blowing-up and rescaling argument on nonlocal elliptic equations." International Journal of Mathematics 27, no. 08 (July 2016): 1650064. http://dx.doi.org/10.1142/s0129167x16500646.

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In this paper, we develop a direct blowing-up and rescaling argument for nonlinear equations involving nonlocal elliptic operators including the fractional Laplacian. Instead of using the conventional extension method introduced by Caffarelli and Silvestre to localize the problem, we work directly on the nonlocal operator. Using the defining integral, by an elementary approach, we carry on a blowing-up and rescaling argument directly on the nonlocal equations and thus obtain a priori estimates on the positive solutions. Based on this estimate and the Leray–Schauder degree theory, we establish the existence of positive solutions. We believe that the ideas introduced here can be applied to problems involving more general nonlocal operators.
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Dissertations / Theses on the topic "Schauder estimate"

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MARINO, LORENZO. "Regolarizzazione debole attraverso rumore di Lévy degenere e sue applicazioni." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2021. http://hdl.handle.net/10281/330542.

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Dopo un'introduzione generale sul fenomeno della regolarizzazione attraverso rumore in un contesto degenere, la prima parte di questa tesi si concentra nello stabilire le stime di Schauder, un strumento analitico utile per dimostrare anche il carattere ben posto di equazioni differenziali stocastiche (EDS), per due classi di equazioni di Kolmogorov sotto una condizione di tipo Hörmander debole, i cui coefficienti giacciono in opportuni spazi di Hölder anisotropi con multi-indici di regolarità. La prima classe considera un sistema non lineare controllato da un operatore simmetrico ⍺-stabile che agisce solo su alcune componenti. Il nostro metodo di dimostrazione si basa su un approccio perturbativo basato su espansioni della parametrice progressiva tramite formule di tipo Duhamel. A causa delle scarse proprietà regolarizzanti date dal contesto degenere, sfruttiamo anche alcuni controlli sulle norme di Besov, per trattare la perturbazione non lineare. Come estensione del primo modello, presentiamo anche delle stime di Schauder associate a un operatore di Ornstein-Uhlenbeck degenere guidato da una classe più ampia di operatori di tipo quasi-stabile, come quello stabile relativistico o quello di Lamperti. La dimostrazione di questo risultato si basa invece su un'analisi precisa del comportamento del semigruppo di Markov corrispondente tra spazi di Hölder anisotropici e alcune tecniche di interpolazione. Sfruttando un approccio della parametrice retrograda, la seconda parte di questa tesi cerca di stabilire il carattere ben posto in senso debole per una catena degenere di EDS guidate dalla stessa classe di processi quasi-stabili, sotto le assunzioni di regolarità di Hölder minime per i coefficienti. Come corollario del nostro metodo, presentiamo anche stime di tipo Krylov di interesse indipendente per il processo canonico sottostante. Infine, sottolineiamo attraverso opportuni controesempi che esiste effettivamente una soglia (quasi) ottimale sugli esponenti di regolarità che garantiscono il carattere ben posto debole per l'EDS. In relazione ad alcune applicazioni meccaniche per delle dinamiche cinetiche con attrito, concludiamo studiando la stabilità delle perturbazioni del secondo ordine per operatori degeneri di Kolmogorov nelle norme Lp e Hölder.
After a general introduction about the regularization by noise phenomenon in the degenerate setting, the first part of this thesis focuses at establishing the Schauder estimates, a useful analytical tool to prove also the well-posedness of stochastic differential equations (SDEs), for two different classes of Kolmogorov equations under a weak Hörmander-like condition, whose coefficients lie in suitable anisotropic Hölder spaces with multi-indices of regularity. The first class considers a nonlinear system controlled by a symmetric ⍺-stable operator acting only on some components. Our method of proof relies on a perturbative approach based on forward parametrix expansions through Duhamel-type formulas. Due to the low regularizing properties given by the degenerate setting, we also exploit some controls on Besov norms, in order to deal with the non-linear perturbation. As an extension of the first one, we also present Schauder estimates associated with a degenerate Ornstein-Uhlenbeck operator driven by a larger class of ⍺-stable-like operators, like the relativistic or the Lamperti stable one. The proof of this result relies instead on a precise analysis of the behaviour of the associated Markov semigroup between anisotropic Hölder spaces and some interpolation techniques. Exploiting a backward parametrix approach, the second part of this thesis aims at establishing the well-posedness in a weak sense of a degenerate chain of SDEs driven by the same class of ⍺-stable-like processes, under the assumptions of the minimal Hölder regularity on the coefficients. As a by-product of our method, we also present Krylov-type estimates of independent interest for the associated canonical process. Finally, we emphasize through suitable counter-examples that there exists indeed an (almost) sharp threshold on the regularity exponents ensuring the weak well-posedness for the SDE. In connection with some mechanical applications for kinetic dynamics with friction, we conclude by investigating the stability of second-order perturbations for degenerate Kolmogorov operators in Lp and Hölder norms.
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Ayed, Hela. "Analyse d'un problème d'interaction fluide-structure avec des conditions aux limites de type frottement à l'interface." Thesis, Normandie, 2017. http://www.theses.fr/2017NORMC213/document.

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Cette thèse est consacrée à l'analyse mathématique et numérique d'un problème d'interaction fluide-structure stationnaire, couplant un fluide newtonien, visqueux et incompressible, modélisé par les équations de Stokes 2D et une structure déformable, décrite par les équations d'une poutre 1D. Le fluide et la structure sont couplés via une condition aux limites de type frottement à l'interface.Dans l'étude théorique, nous montrons un résultat d'existence et unicité de solutions faibles, dans le cadre de petits déplacements, du problème de couplage fluide structure avec une condition de glissement de type Tresca en utilisant le théorème de point fixe de Schauder.Dans l'analyse numérique, nous étudions d'abord, l'approximation du problème de Stokes avec la condition de Tresca par une méthode d'éléments finis mixtes à quatre champs. Nous montrons ensuite une estimation d'erreur a priori optimale pour des données régulières et nous réalisons des tests numériques. Enfin, nous présentons un algorithme de point fixe pour la simulation numérique du problème couplé avec des conditions aux limites non linéaires
This PHD thesis is devoted to the theoretical and numerical analysis of a stationary fluid-structure interaction problem between an incompressible viscous Newtonian fluid, modeled by the 2D Stokes equations, and a deformable structure modeled by the 1D beam equations.The fluid and structure are coupled via a friction boundary condition at the fluid-structure interface.In the theoretical study, we prove the existence of a unique weak solution, under small displacements, of the fluid-structure interaction problem under a slip boundary condition of friction type (SBCF) by using Schauder fixed point theorem.In the numerical analysis, we first study a mixed finite element approximation of the Stokes equations under SBCF.We also prove an optimal a priori error estimate for regular data and we provide numerical examples.Finally, we present a fixed point algorithm for numerical simulation of the coupled problem under nonlinear boundary conditions
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Bucur, C. D. "SOME NONLOCAL OPERATORS AND EFFECTS DUE TO NONLOCALITY." Doctoral thesis, Università degli Studi di Milano, 2017. http://hdl.handle.net/2434/488032.

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In this thesis, we deal with problems related to nonlocal operators, in particular to the fractional Laplacian and some other types of fractional derivatives. We make an extensive introduction to the fractional Laplacian and to some related contemporary research themes. We add to this some original material: the potential theory of this operator and a proof of Schauder estimates with the potential theory approach, the study of a fractional elliptic problem in $mathbb{R}^n$ with convex nonlinearities and critical growth, and a stickiness property of $s$-minimal surfaces as $s$ gets small. Also, focusing our attention on some particular traits of the fractional Laplacian, we prove that other fractional operators have a similar behavior: Caputo stationary functions satisfy a particular density property in the space of smooth functions; an extension operator can be build for Marchaud-stationary functions.
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Marino, Greta. "A-priori estimates for some classes of elliptic problems." Doctoral thesis, Università di Catania, 2019. http://hdl.handle.net/10761/4116.

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L'obiettivo di questa tesi è di studiare alcuni aspetti di un potente strumento ampiamente utilizzato in analisi matematica, che è rappresentato dalle stime a priori. Infatti, le stime a priori hanno un ruolo chiave nella teoria delle equazioni differenziali a derivate parziali e nel calcolo delle variazioni, perché sono intimamente legate all'esistenza di soluzione per un dato problema. Nella tesi vengono presentati tre lavori scritti durante il periodo del dottorato, in ciascuno dei quali vengono utilizzate le stime a priori. Il primo lavoro, scritto in collaborazione con il Prof. S. Mosconi, riguarda l'esistenza di soluzione per la seguente equazione differenziale ordinaria del quarto ordine (equazione di Swift-Hohenberg), $ u''''+ qu''+ F'(u)= 0$, dove $q$ è un parametro reale e $F$ è una funzione $C^2$, coerciva e quasi-convessa. Il secondo lavoro, scritto in collaborazione con il prof. P. Winkert, riguarda stime a priori per un problema ellittico in cui gli operatori hanno crescita critica, sia nel dominio che sulla frontiera. Il terzo lavoro, scritto in collaborazione con i Prof. S.A. Marano e A. Moussaoui, riguarda l'esistenza di soluzione per un sistema ellittico definito in tutto lo spazio $\R^N$, in cui le nonlinearità contengono termini singolari, cioè che possono tendere a $+\infty$ quando la variabile tende a zero.
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Nascimento, Moisés Aparecido do. "Resultados do tipo Ambrosetti-Prodi para problemas quasilineares." Universidade Federal de São Carlos, 2015. https://repositorio.ufscar.br/handle/ufscar/7640.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
We present results of Ambrosseti-Prodi type to quasilinear problems involving the p-Laplace operator. We consider the scalar case and a a problem with systems of equations. In the scalar case, we work with the conditions of Neumann and Dirichlet. In the problem involving system, we consider the condition og Dirichlet. In order to get the results we use the theory of Leray-Schauder degree and a priori estimates.
Neste trabalho apresentamos resultados do tipo Ambrosseti-Prodi para problemas quasilineares envolvendo o aperador p-Laplaciano. Considerando o caso escalar eu um problema com sistemas de equações. Para os casos escalares, trabalhamos com a condições de Neumann e Dirichlet, já para o problema envolvendo sistema, consideramos a condição Dirichlet. Para obter mais resultados usamos a teoria do grau de Leray-Schauder e estimativas a priori.
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Fino, Ahmad. "Contributions aux problèmes d'évolution." Phd thesis, Université de La Rochelle, 2010. http://tel.archives-ouvertes.fr/tel-00437141.

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Dans cette thèse, nous nous intéressons à l'étude de trois équations aux dérivées partielles et d'évolution non-locales en espace et en temps. Les solutions de ces trois solutions peuvent exploser en temps fini. Dans une première partie de cette thèse, nous considérons l'équation de la chaleur nonlinéaire avec une puissance fractionnaire du laplacien, et obtenons notamment que, dans le cas d'exposant sur-critique, le comportement asymptotique de la solution lorsque $t\rightarrow+\infty$ est déterminé par le terme de diffusion anormale. D'autre part, dans le cas d'exposant sous-critique, l'effet du terme non-linéaire domine. Dans une deuxième partie, nous étudions une équation parabolique avec le laplacien fractionnaire et un terme non-linéaire et non-local en temps. On montre que la solution est globale dans le cas sur-critique pour toute donnée initiale ayant une mesure assez petite, tandis que dans le cas sous-critique, on montre que la solution explose en temps fini $T_{\max}>0$ pour toute condition initiale positive et non-triviale. Dans ce dernier cas, on cherche le comportement de la norme $L^1$ de la solution en précisant le taux d'explosion lorsque $t$ s'approche du temps d'explosion $T_{\max}.$ Nous cherchons encore les conditions nécessaires à l'existence locale et globale de la solution. Une toisième partie est consacré à une généralisation de la deuxième partie au cas de systèmes $2\times 2$ avec le laplacien ordinaire. On étudie l'existence locale de la solution ainsi qu'un résultat sur l'explosion de la solution avec les mêmes propriétés étudiées dans le troisième chapitre. Dans la dernière partie, nous étudions une équation hyperbolique dans $\mathbb{R}^N,$ pour tout $N\geq2,$ avec un terme non-linéaire non-local en temps. Nous obtenons un résultat d'existence locale de la solution sous des conditions restrictives sur les données initiales, la dimension de l'espace et les exposants du terme non-linéaire. De plus on obtient, sous certaines conditions sur les exposants, que la solution explose en temps fini, pour toute condition initiale ayant de moyenne strictement positive.
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Archalousová, Olga. "Singulární počáteční úloha pro obyčejné diferenciální a integrodiferenciální rovnice." Doctoral thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2011. http://www.nusl.cz/ntk/nusl-233525.

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The thesis deals with qualitative properties of solutions of singular initial value problems for ordinary differential and integrodifferential equations which occur in the theory of linear and nonlinear electrical circuits and the theory of therminionic currents. The research is concentrated especially on questions of existence and uniqueness of solutions, asymptotic estimates of solutions and modications of Adomian decomposition method for singular initial problems. Solution algoritms are derived for scalar differential equations of Lane-Emden type using Taylor series and modication of the Adomian decomposition method. For certain classes of nonlinear of integrodifferential equations asymptotic expansions of solutions are constructed in a neighbourhood of a singular point. By means of the combination of Wazewski's topological method and Schauder xed-point theorem there are proved asymptotic estimates of solutions in a region which is homeomorphic to a cone having vertex coinciding with the initial point. Using Banach xed-point theorem the uniqueness of a solution of the singular initial value problem is proved for systems of integrodifferential equations of Volterra and Fredholm type including implicit systems. Moreover, conditions of continuous dependence of a solution on a parameter are determined. Obtained results are presented in illustrative examples.
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Ching, Tsai Shu, and 蔡淑靖. "Schauder's Estimates for the Parabolic Equation." Thesis, 1993. http://ndltd.ncl.edu.tw/handle/57948794998720095848.

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碩士
國立中正大學
應用數學研究所
81
In this paper, we prove two uniqueness theorems and prove the istence of solution for Cauchy problem and its Schauder'ss. The first theorem is concerned to the uniqueness ofquation, the second theorem is concerned tp theeat equation. The last theorem is concerned to thee solution and its Schauder's estimates for Cauchy problem. Moreover, by uniqueness theorem, we know that theres a constant c satisfying the Schauder's estimates for then of Cauchy problem.
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Pu-ZhaoKow and 邱普照. "Schauder's Estimates and Asymptotic Behavior of Solutions of the Stationary Navier-Stokes Equation in an Exterior Domain." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/muhqpe.

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Books on the topic "Schauder estimate"

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König, Manfred. Schauder's estimates and boundary value problems for quasilinear partial differential equations. Montréal, Québec, Canada: Presses de l'Université de Montréal, 1985.

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Schauder's estimates and boundary value problems for quasilinear partial differential equations. Montréal, Québec, Canada: Presses de l'Université Montréal, 1985.

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Epstein, Charles L., and Rafe Mazzeo. Existence of Solutions. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691157122.003.0010.

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This chapter proves existence of solutions to the inhomogeneous problem using the Schauder estimate and analyzes a generalized Kimura diffusion operator, L, defined on a manifold with corners, P. The discussion centers on the solution w = v + u, where v solves the homogeneous Cauchy problem with v(x, 0) = f(x) and u solves the inhomogeneous problem with u(x, 0) = 0. The chapter first provides definitions for the Wright–Fisher–Hölder spaces on a general compact manifold with corners before explaining the steps involved in the existence proof. It then verifies the induction hypothesis and treats the k = 0 case. It also shows how to perform the doubling construction for P and considers the existence of the resolvent operator and a contraction semi-group. Finally, it discusses the problem of higher regularity.
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Epstein, Charles L., and Rafe Mazzeo. Holder Estimates for the 1-dimensional Model Problems. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691157122.003.0006.

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This chapter establishes Hölder space estimates for the 1-dimensional model problems. It gives a detailed treatment of the 1-dimensional case, in part because all of the higher dimensional estimates are reduced to estimates on heat kernels for the 1-dimensional model problems. It also presents the proof of parabolic Schauder estimates for the generalized Kimura diffusion operator using the explicit formula for the heat kernel, along with standard tools of analysis. Finally, it considers kernel estimates for degenerate model problems, explains how Hölder estimates are obtained for the 1-dimensional model problems, and describes the properties of the resolvent operator.
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Konig, Manfred. Schauder's Estimates and Boundary Value Problems for Quasilinear Partial Differential Equations (Seminaire de mathematiques superieures). Gaetan Morin Editeur Ltee, 1985.

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Book chapters on the topic "Schauder estimate"

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Giaquinta, Mariano, and Luca Martinazzi. "Schauder estimates." In An Introduction to the Regularity Theory for Elliptic Systems, Harmonic Maps and Minimal Graphs, 75–95. Pisa: Scuola Normale Superiore, 2012. http://dx.doi.org/10.1007/978-88-7642-443-4_5.

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Taylor, Michael E. "Extension of the Schauder estimates." In Pseudodifferential Operators and Nonlinear PDE, 178–82. Boston, MA: Birkhäuser Boston, 1991. http://dx.doi.org/10.1007/978-1-4612-0431-2_11.

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Krylov, N. V., and E. Priola. "Poisson Stochastic Process and Basic Schauder and Sobolev Estimates in the Theory of Parabolic Equations (Short Version)." In Stochastic Partial Differential Equations and Related Fields, 201–11. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-74929-7_10.

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"Schauder estimates and applications." In Translations of Mathematical Monographs, 163–82. Providence, Rhode Island: American Mathematical Society, 1992. http://dx.doi.org/10.1090/mmono/099/07.

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Kichenassamy, Satyanad. "Chapter 5 Schauder-type estimates and applications." In Handbook of Differential Equations: Stationary Partial Differential Equations, 401–64. Elsevier, 2006. http://dx.doi.org/10.1016/s1874-5733(06)80009-4.

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"Chapter 15. Schauder Estimates For Beltrami Operators." In Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane (PMS-48), 389–402. Princeton University Press, 2008. http://dx.doi.org/10.1515/9781400830114.389.

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"Schauder's Estimates for Linear Elliptic Equations." In Elliptic and Parabolic Equations, 159–96. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812772800_0006.

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"Schauder's Estimates for Linear Parabolic Equations." In Elliptic and Parabolic Equations, 197–232. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812772800_0007.

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Lunardi, Alessandra, and Vincenzo Vespri. "Optimal L ∞ and Schauder Estimates for Elliptic and Parabolic Operators with Unbounded Coefficients." In Reaction Diffusion Systems, 217–39. CRC Press, 2020. http://dx.doi.org/10.1201/9781003072195-18.

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Bilalov, Bilal, Sabina Sadigova, and Zaur Kasumov. "Some Solvability Problems of Differential Equations in Non-standard Sobolev Spaces." In Differential Equations [Working Title]. IntechOpen, 2022. http://dx.doi.org/10.5772/intechopen.104918.

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In this chapter an m-th order elliptic equation is considered in Sobolev spaces generated by the norm of a grand Lebesgue space. Subspaces are determined in which the shift operator is continuous, and local solvability (in the strong sense) is established in these subspaces. It is established an interior and up-to boundary Schauder-type estimates with respect to these Sobolev spaces for m-th order elliptic operators, the trace of functions and trace operator are determined, the boundedness of trace operator and the extension theorem are proved, the properties of the Riesz potential are studied regarding these Sobolev spaces, etc. It is considered a second-order elliptic equation, and we study the Fredholmness of the Dirichlet problem in the Sobolev space generated by a separable subspace of the grand Lebesgue space. It is also considered one spectral problem for a discontinuous second-order differential operator and proved the theorem on the basicity of eigenfunctions of this operator in subspace of Morrey space, in which the infinitely differentiable functions with compact support are dense.
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