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Journal articles on the topic 'Schauder estimate'

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Published: 9 March 2023
Last updated: 10 March 2023

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

Choi, Nari. "The existence of solutions for the gravitational Maxwell gauged O(3) model on compact surfaces." Journal of Mathematical Physics 63, no. 8 (August 1, 2022): 081506. http://dx.doi.org/10.1063/5.0060304.

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We consider an elliptic equation induced from the Maxwell gauged O(3) sigma model coupled with gravity. In particular, we study the main equation as two cases: one is for only string and the other is for anti-string. On the compact surface, we prove the existence of ɛ-dependent solutions for each case by using the super-sub solutions method. Moreover, we find the second solution by using the Leray–Schauder degree theory. Furthermore, we estimate the asymptotic behavior of our solution as ɛ → 0.
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12

Korpusov, M. O., and D. K. Yablochkin. "Potential Theory and Schauder Estimate in Hölder Spaces for (3 + 1)-Dimensional Benjamin–Bona–Mahoney–Burgers Equation." Computational Mathematics and Mathematical Physics 61, no. 8 (August 2021): 1289–314. http://dx.doi.org/10.1134/s0965542521060051.

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13

Marano, Salvatore A. "A remark on a third-order three-point boundary value problem." Bulletin of the Australian Mathematical Society 49, no. 1 (February 1994): 1–5. http://dx.doi.org/10.1017/s0004972700016014.

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Let f be a real function defined on [0, 1] × R3 and let η ∈ (0, 1). Very recently, C.P. Gupta and V. Lakshimikantham, making use of the Leray-Schauder continuation theorem and Wirtinger-type inequalities, established an existence result for the problem(Theorem 1 and Remark 4 of [Nonlinear Anal. 16 (1991), 949–957]).The aim of the present paper is simply to point out how, bu means of a completely different approach, it is possible to improve that result not only by requiring much general on f, but also by giving a precise pointwise estimate on x″′
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14

Yaying, Taja, Bipan Hazarika, and S. A. Mohiuddine. "Domain of Padovan q-difference matrix in sequence spaces lp and l∞." Filomat 36, no. 3 (2022): 905–19. http://dx.doi.org/10.2298/fil2203905y.

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In this study, we construct the difference sequence spaces lp (P?2q) = (lp)P?2q, 1 ? p ? ?, where P = (?rs) is an infinite matrix of Padovan numbers %s defined by ?rs = {?s/?r+5-2 0 ? s ? r, 0 s > r. and ?2q is a q-difference operator of second order. We obtain some inclusion relations, topological properties, Schauder basis and ?-, ?- and ?-duals of the newly defined space. We characterize certain matrix classes from the space lp (P?2q) to any one of the space l1, c0, c or l?. We examine some geometric properties and give certain estimation for von-Neumann Jordan constant and James constant of the space lp(P). Finally, we estimate upper bound for Hausdorff matrix as a mapping from lp to lp(P).
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15

Simon, Leon. "Schauder estimates by scaling." Calculus of Variations and Partial Differential Equations 5, no. 5 (July 1, 1997): 391–407. http://dx.doi.org/10.1007/s005260050072.

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16

de Borbon, Martin, and Gregory Edwards. "Schauder estimates on products of cones." Commentarii Mathematici Helvetici 96, no. 1 (March 12, 2021): 113–48. http://dx.doi.org/10.4171/cmh/509.

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17

Clément, Ph, G. Gripenberg, and S.-O. Londen. "Schauder estimates for equationswith fractional derivatives." Transactions of the American Mathematical Society 352, no. 5 (February 14, 2000): 2239–60. http://dx.doi.org/10.1090/s0002-9947-00-02507-1.

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18

Baderko, Elena A. "Schauder estimates for oblique derivative problems." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 326, no. 12 (June 1998): 1377–80. http://dx.doi.org/10.1016/s0764-4442(98)80395-9.

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19

Gutiérrez, Cristian E., and Ermanno Lanconelli. "Schauder estimates for sub-elliptic equations." Journal of Evolution Equations 9, no. 4 (July 31, 2009): 707–26. http://dx.doi.org/10.1007/s00028-009-0030-x.

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20

Wigley, Neil M. "Schauder estimates in domains with corners." Archive for Rational Mechanics and Analysis 104, no. 3 (September 1988): 271–76. http://dx.doi.org/10.1007/bf00281357.

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21

Wiegner, Michael. "Schauder estimates for boundary layer potentials." Mathematical Methods in the Applied Sciences 16, no. 12 (December 1993): 877–94. http://dx.doi.org/10.1002/mma.1670161204.

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22

Chen, Huyuan, Mouhamed Moustapha Fall, and Binling Zhang. "On isolated singularities of Kirchhoff equations." Advances in Nonlinear Analysis 10, no. 1 (May 27, 2020): 102–20. http://dx.doi.org/10.1515/anona-2020-0103.

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Abstract In this note, we study isolated singular positive solutions of Kirchhoff equation $$\begin{array}{} \displaystyle M_\theta(u)(-{\it\Delta}) u =u^p \quad{\rm in}\quad {\it\Omega}\setminus \{0\},\qquad u=0\quad {\rm on}\quad \partial {\it\Omega}, \end{array}$$ where p > 1, θ ∈ ℝ, Mθ(u) = θ + ∫Ω |∇ u| dx, Ω is a bounded smooth domain containing the origin in ℝN with N ≥ 2. In the subcritical case: 1 < p < $\begin{array}{} \displaystyle \frac{N}{N-2} \end{array}$ if N ≥ 3, 1 < p < + ∞ if N = 2, we employee the Schauder fixed point theorem to derive a sequence of positive isolated singular solutions for the above equation such that Mθ(u) > 0. To estimate Mθ(u), we make use of the rearrangement argument. Furthermore, we obtain a sequence of isolated singular solutions such that Mθ(u) < 0, by analyzing relationship between the parameter λ and the unique solution uλ of $$\begin{array}{} \displaystyle -{\it\Delta} u+\lambda u^p=k\delta_0\quad{\rm in}\quad B_1(0),\qquad u=0\quad {\rm on}\quad \partial B_1(0). \end{array}$$ In the supercritical case: $\begin{array}{} \displaystyle \frac{N}{N-2} \end{array}$ ≤ p < $\begin{array}{} \displaystyle \frac{N+2}{N-2} \end{array}$ with N ≥ 3, we obtain two isolated singular solutions ui with i = 1, 2 such that Mθ(ui) > 0 under other assumptions.
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23

陈, 雯雯. "Schauder Estimates for the Solutions of the Heat Equation." Pure Mathematics 04, no. 05 (2014): 208–17. http://dx.doi.org/10.12677/pm.2014.45030.

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24

Jin, Tianling, and Jingang Xiong. "Schauder estimates for nonlocal fully nonlinear equations." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 33, no. 5 (September 2016): 1375–407. http://dx.doi.org/10.1016/j.anihpc.2015.05.004.

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25

Marino, Lorenzo. "Schauder estimates for degenerate stable Kolmogorov equations." Bulletin des Sciences Mathématiques 162 (September 2020): 102885. http://dx.doi.org/10.1016/j.bulsci.2020.102885.

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26

Wang, Xu-Jia. "Schauder Estimates for Elliptic and Parabolic Equations*." Chinese Annals of Mathematics, Series B 27, no. 6 (November 2006): 637–42. http://dx.doi.org/10.1007/s11401-006-0142-3.

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27

Solonnikov, Vsevolod A. "Weighted Schauder estimates for Evolution Stokes Problem." ANNALI DELL'UNIVERSITA' DI FERRARA 52, no. 1 (July 2006): 137–72. http://dx.doi.org/10.1007/s11565-006-0012-7.

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28

Lieberman, Gary M. "Intermediate Schauder estimates for oblique derivative problems." Archive for Rational Mechanics and Analysis 93, no. 2 (1986): 129–34. http://dx.doi.org/10.1007/bf00279956.

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29

元, 琛. "Schauder Estimates for Parabolic Baouendi-Grushin Laplace Equations." Pure Mathematics 10, no. 12 (2020): 1229–39. http://dx.doi.org/10.12677/pm.2020.1012146.

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30

Marino, Lorenzo. "Schauder estimates for degenerate Lévy Ornstein-Uhlenbeck operators." Journal of Mathematical Analysis and Applications 500, no. 1 (August 2021): 125168. http://dx.doi.org/10.1016/j.jmaa.2021.125168.

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31

Ma, Feiyao, and Lihe Wang. "Schauder type estimates of linearized Mullins-Sekerka problem." Communications on Pure & Applied Analysis 11, no. 3 (2012): 1037–50. http://dx.doi.org/10.3934/cpaa.2012.11.1037.

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32

Guo, Bin, and Jian Song. "Schauder estimates for equations with cone metrics, I." Indiana University Mathematics Journal 70, no. 5 (2021): 1639–76. http://dx.doi.org/10.1512/iumj.2021.70.7852.

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33

Kuo, Hung-Ju, and Neil S. Trudinger. "Schauder estimates for fully nonlinear elliptic difference operators." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 132, no. 6 (December 2002): 1395–406. http://dx.doi.org/10.1017/s030821050000216x.

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In this paper, we are concerned with discrete Schauder estimates for solutions of fully nonlinear elliptic difference equations. Our estimates are discrete versions of second derivative Hölder estimates of Evans, Krylov and Safonov for fully nonlinear elliptic partial differential equations. They extend previous results of Holtby for the special case of functions of pure second-order differences on cubic meshes. As with Holtby's work, the fundamental ingredients are the pointwise estimates of Kuo-Trudinger for linear difference schemes on general meshes.
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34

Hao, Zimo, Mingyan Wu, and Xicheng Zhang. "Schauder estimates for nonlocal kinetic equations and applications." Journal de Mathématiques Pures et Appliquées 140 (August 2020): 139–84. http://dx.doi.org/10.1016/j.matpur.2020.06.003.

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35

Wang, Yuxing, and Kai Du. "Schauder-type estimates for higher-order parabolic SPDEs." Journal of Evolution Equations 20, no. 4 (February 19, 2020): 1453–83. http://dx.doi.org/10.1007/s00028-020-00562-5.

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36

WEI, Na, Yongsheng JIANG, and Yonghong WU. "Partial schauder estimates for a sub-elliptic equation." Acta Mathematica Scientia 36, no. 3 (May 2016): 945–56. http://dx.doi.org/10.1016/s0252-9602(16)30051-0.

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37

Breit, D., A. Cianchi, L. Diening, and S. Schwarzacher. "Global Schauder Estimates for the $$\mathbf {p}$$-Laplace System." Archive for Rational Mechanics and Analysis 243, no. 1 (November 24, 2021): 201–55. http://dx.doi.org/10.1007/s00205-021-01712-w.

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AbstractAn optimal first-order global regularity theory, in spaces of functions defined in terms of oscillations, is established for solutions to Dirichlet problems for the p-Laplace equation and system, with the right-hand side in divergence form. The exact mutual dependence among the regularity of the solution, of the datum on the right-hand side, and of the boundary of the domain in these spaces is exhibited. A comprehensive formulation of our results is given in terms of Campanato seminorms. New regularity results in customary function spaces, such as Hölder, $$\text {BMO}$$ BMO and $${{\,\mathrm{VMO}\,}}$$ VMO spaces, follow as a consequence. Importantly, the conclusions are new even in the linear case when $$p=2$$ p = 2 , and hence the differential operator is the plain Laplacian. Yet in this classical linear setting, our contribution completes and augments the celebrated Schauder theory in Hölder spaces. A distinctive trait of our results is their sharpness, which is demonstrated by a family of apropos examples.
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38

Bramanti, Marco, and Luca Brandolini. "Schauder estimates for parabolic nondivergence operators of Hörmander type." Journal of Differential Equations 234, no. 1 (March 2007): 177–245. http://dx.doi.org/10.1016/j.jde.2006.07.015.

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39

Boccia, Serena. "Schauder estimates for solutions of higher-order parabolic systems." Methods and Applications of Analysis 20, no. 1 (2013): 47–68. http://dx.doi.org/10.4310/maa.2013.v20.n1.a3.

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40

Deuring, Paul, and Werner Varnhorn. "Schauder Estimates for the Single Layer Potential in Hydrodynamics." Mathematische Nachrichten 157, no. 1 (1992): 277–89. http://dx.doi.org/10.1002/mana.19921570123.

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41

Yao, Feng-ping, and Shu-lin Zhou. "Schauder estimates for parabolic equation of bi-harmonic type." Applied Mathematics and Mechanics 28, no. 11 (November 2007): 1503–16. http://dx.doi.org/10.1007/s10483-007-1110-z.

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42

Priola, Enrico. "Global Schauder estimates for a class of degenerate Kolmogorov equations." Studia Mathematica 194, no. 2 (2009): 117–53. http://dx.doi.org/10.4064/sm194-2-2.

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43

Dong, Hongjie, and Doyoon Kim. "Schauder estimates for a class of non-local elliptic equations." Discrete & Continuous Dynamical Systems - A 33, no. 6 (2013): 2319–47. http://dx.doi.org/10.3934/dcds.2013.33.2319.

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44

Jin, Tianling, and Jingang Xiong. "Schauder estimates for solutions of linear parabolic integro-differential equations." Discrete and Continuous Dynamical Systems 35, no. 12 (May 2015): 5977–98. http://dx.doi.org/10.3934/dcds.2015.35.5977.

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45

Beanland, Kevin, Daniel Freeman, and Rui Liu. "Upper and lower estimates for Schauder frames and atomic decompositions." Fundamenta Mathematicae 231, no. 2 (2015): 161–88. http://dx.doi.org/10.4064/fm231-2-4.

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46

Yi, Cao, and Li Dongsheng. "Partial Schauder estimates for ellipticand parabolic equations of second order." SCIENTIA SINICA Mathematica 48, no. 1 (November 9, 2017): 15. http://dx.doi.org/10.1360/n012017-00091.

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47

Troianiello, Giovanni Maria. "Estimates of the Caccioppoli-Schauder type in weighted function spaces." Transactions of the American Mathematical Society 334, no. 2 (February 1, 1992): 551–73. http://dx.doi.org/10.1090/s0002-9947-1992-1049865-3.

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48

Chaudru de Raynal, Paul-Éric, Stéphane Menozzi, and Enrico Priola. "Schauder estimates for drifted fractional operators in the supercritical case." Journal of Functional Analysis 278, no. 8 (May 2020): 108425. http://dx.doi.org/10.1016/j.jfa.2019.108425.

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49

Han, Qing. "Schauder estimates for elliptic operators with applications to nodal sets." Journal of Geometric Analysis 10, no. 3 (September 2000): 455–80. http://dx.doi.org/10.1007/bf02921945.

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50

Lieberman, Gary M. "Intermediate Schauder theory for second order parabolic equations. I. Estimates." Journal of Differential Equations 63, no. 1 (June 1986): 1–31. http://dx.doi.org/10.1016/0022-0396(86)90052-5.

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