Dissertations / Theses on the topic 'Sobolev spaces'
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Clemens, Jason. "Sobolev spaces." Kansas State University, 2014. http://hdl.handle.net/2097/18186.
Full textDepartment of Mathematics
Marianne Korten
The goal for this paper is to present material from Gilbarg and Trudinger’s Elliptic Partial Differential Equations of Second Order chapter 7 on Sobolev spaces, in a manner easily accessible to a beginning graduate student. The properties of weak derivatives and there relationship to conventional concepts from calculus are the main focus, that is when do weak and strong derivatives coincide. To enable the progression into the primary focus, the process of mollification is presented and is widely used in estimations. Imbedding theorems and compactness results are briefly covered in the final sections. Finally, we add some exercises at the end to illustrate the use of the ideas presented throughout the paper.
Gjestland, Fredrik Joachim. "Distributions, Schwartz Space and Fractional Sobolev Spaces." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, 2013. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-23452.
Full textKydyrmina, Nurgul. "Operators in Sobolev Morrey spaces." Doctoral thesis, Università degli studi di Padova, 2013. http://hdl.handle.net/11577/3423455.
Full textGli spazi di Morrey sono stati introdotti da Charles Morrey nel 1938. Essi sono uno strumento utile nella teoria della regolarità per equazioni differenziali alle derivate parziali, in analisi reale ed in fisica matematica. Negli anni novanta del XX secolo ha iniziato a svilupparsi un attivo studio degli spazi di Morrey di tipo generalizzato che sono caratterizzati da un parametro funzionale. E' stato ottenuto un cero numero di risultati sulla limitatezza degli operatori classici negli spazi di Morrey di tipo generalizzato. All'inizio del XXI secolo ci sono stati nuovi e attivi sviluppi in questa area. Nell'ultima decade molti matematici hanno svolto ricerche su spazi funzionali relativi agli spazi di Morrey. Tra questi spazi gli spazi di tipo Sobolev giocano un ruolo importante. Nella tesi si studiano Spazi di Sobolev costruiti su spazi di Morrey, anche detti spazi di Sobolev Morrey. Questi sono spazi di funzioni che hanno derivate fino ad un certo ordine negli spazi di Morrey. Si analizzano alcune proprietà di base degli spazi di Morrey e degli spazi di Sobolev-Morrey. Poi si considerano operatori di immersione e di moltiplicazione negli spazi di Sobolev Morrey. La terza parte della tesi presenta uno studio degli operatori di composizione negli spazi di Sobolev Morrey. I risultati presentati nella tesi sono stati ottenuti sotto la supervisione dei Professori V.I. Burenkov and M. Lanza de Cristoforis.
Färm, David. "Upper gradients and Sobolev spaces on metric spaces." Thesis, Linköping University, Department of Mathematics, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-5816.
Full textThe Laplace equation and the related p-Laplace equation are closely associated with Sobolev spaces. During the last 15 years people have been exploring the possibility of solving partial differential equations in general metric spaces by generalizing the concept of Sobolev spaces. One such generalization is the Newtonian space where one uses upper gradients to compensate for the lack of a derivative.
All papers on this topic are written for an audience of fellow researchers and people with graduate level mathematical skills. In this thesis we give an introduction to the Newtonian spaces accessible also for senior undergraduate students with only basic knowledge of functional analysis. We also give an introduction to the tools needed to deal with the Newtonian spaces. This includes measure theory and curves in general metric spaces.
Many of the properties of ordinary Sobolev spaces also apply in the generalized setting of the Newtonian spaces. This thesis includes proofs of the fact that the Newtonian spaces are Banach spaces and that under mild additional assumptions Lipschitz functions are dense there. To make them more accessible, the proofs have been extended with comments and details previously omitted. Examples are given to illustrate new concepts.
This thesis also includes my own result on the capacity associated with Newtonian spaces. This is the theorem that if a set has p-capacity zero, then the capacity of that set is zero for all smaller values of p.
Park, Young Ja. "Sobolev trace inequality and logarithmic Sobolev trace inequality." Digital version:, 2000. http://wwwlib.umi.com/cr/utexas/fullcit?p9992883.
Full textSpector, Daniel. "Characterization of Sobolev and BV Spaces." Research Showcase @ CMU, 2011. http://repository.cmu.edu/dissertations/78.
Full textNeves, Julio Severino. "Fractional Sobolev-type spaces and embeddings." Thesis, University of Sussex, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.341514.
Full textDines, Nicoleta, Gohar Harutjunjan, and Bert-Wolfgang Schulze. "The Zaremba problem in edge Sobolev spaces." Universität Potsdam, 2003. http://opus.kobv.de/ubp/volltexte/2008/2661/.
Full textDavidsson, Johan. "Sobolev Spaces and the Finite Element Method." Thesis, Örebro universitet, Institutionen för naturvetenskap och teknik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:oru:diva-67470.
Full textClavero, Nadia F. "Optimal Sobolev Embeddings in Spaces with Mixed Norm." Doctoral thesis, Universitat de Barcelona, 2015. http://hdl.handle.net/10803/292613.
Full textThis thesis project concerns estimates, in function spaces, that relate the norm of a function and that of its derivatives. Speci.cally, our main purpose is to study the classical Sobolev-type inequalities due to Gagliardo and Nirenberg for higher order derivatives and more general spaces. In particular, we concentrate on seeking the optimal domains and the optimal ranges for these embeddings between rearrangement-invariant spaces (r.i.) and mixed norm spaces.
Flucher, Martin. "Concentration and compactness of functionals on Sobolev spaces /." [S.l.] : [s.n.], 1991. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=9525.
Full textMekias, Mohamed. "Restriction to hypersurfaces of non-isotropic Sobolev spaces." Thesis, Massachusetts Institute of Technology, 1993. http://hdl.handle.net/1721.1/100868.
Full textAirapetyan, Ruben, and Ingo Witt. "Isometric properties of the Hankel Transformation in weighted sobolev spaces." Universität Potsdam, 1997. http://opus.kobv.de/ubp/volltexte/2008/2500/.
Full textSalvato, Maria. "On the solvability of linear PDEs in weighted Sobolev spaces." Doctoral thesis, Universita degli studi di Salerno, 2012. http://hdl.handle.net/10556/335.
Full textStefani, Giorgio. "A distributional approach to fractional Sobolev spaces and fractional variation." Doctoral thesis, Scuola Normale Superiore, 2020. http://hdl.handle.net/11384/85724.
Full textInahama, Yuzuru. "Logarithmic Sobolev Inequality on Free Loop Groups for Heat Ker-nel Measures Associated with the General Sobolev Spaces." 京都大学 (Kyoto University), 2001. http://hdl.handle.net/2433/150808.
Full textDöhring, Nicolas [Verfasser]. "Regularity of Random Fields in Scales of Besov Spaces and Generalized Sobolev Spaces / Nicolas Döhring." München : Verlag Dr. Hut, 2016. http://d-nb.info/1084386887/34.
Full textBlair, Matthew D. "Strichartz estimates for wave equations with coefficients of Sobolev regularity /." Thesis, Connect to this title online; UW restricted, 2005. http://hdl.handle.net/1773/5745.
Full textGeorgoulis, Emmanuil H. "Discontinuous Galerkin methods on shape-regular and anisotropic meshes." Thesis, University of Oxford, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.270366.
Full textPrats, Soler Martí. "Singular integral operators on sobolev spaces on domains and quasiconformal mappings." Doctoral thesis, Universitat Autònoma de Barcelona, 2015. http://hdl.handle.net/10803/314193.
Full textIn this dissertation some new results on the boundedness of Calderón-Zygmund operators on Sobolev spaces on domains in Rd. First a T(P)-theorem is obtained which is valid for Wn,p (U), where U is a bounded uniform domain of Rd, n is a given natural number and p>d. Essentially, the result obtained states that a convolution Calderón-Zygmund operator is bounded on this function space if and only if T(P) belongs to Wn,p (U) for every polynomial P of degree smaller than n restricted to the domain. For indices p less or equal than d, a sufficient condition for the boundedness in terms of Carleson measures is obtained. In the particular case of n=1 and p<=d, this Carleson condition is shown to be necessary in fact. The case where n is not integer and 0
Schrohe, Elmar, and Jörg Seiler. "Ellipticity and invertibility in the cone algebra on Lp-Sobolev spaces." Universität Potsdam, 1999. http://opus.kobv.de/ubp/volltexte/2008/2562/.
Full textMalý, Lukáš. "Sobolev-Type Spaces : Properties of Newtonian Functions Based on Quasi-Banach Function Lattices in Metric Spaces." Doctoral thesis, Linköpings universitet, Matematik och tillämpad matematik, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-105616.
Full textBuffa, Vito. "Higher order Sobolev Spaces and polyharmonic boundary value problems in Carnot Groups." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2014. http://amslaurea.unibo.it/6893/.
Full textSilvestre, Albero María Pilar. "Capacitary function spaces and applications." Doctoral thesis, Universitat de Barcelona, 2012. http://hdl.handle.net/10803/77717.
Full textLa primera part està dedicada a l’anàlisi d’un espai de capacitat, amb capacitats com a substituts de les mesures en l’estudi d’espais de funcions. L’objectiu és estendre als recicles de funcions associats alguns aspectes de la la teoria d’espais de funcions de Banach, mostrar com la teoria general pot ser aplicada a espais funcionals clàssics com els espais de Lorentz, i completar la teoria d’interpolació real d’aquests espais inclosos en [CeClM] i [Ce]. A la segona part de la tesi es presenta una desigualtat integral que connecta la norma del gradient d’una funció en un espai de funcions amb la integral de la corresponent capacitat del conductor entre dues superfícies de nivell de la funció, que estén les estimacions obtingudes per V. Maz’ya i S. Costea, i desigualtats capacitàries fortes de V. Maz’ya en el cas de la norma de Sobolev. La desigualtat, obtinguda sota condicions de convexitat pel espai funcional, permet una caracterització de les desigualtats de tipus Sobolev per dues mesures, condicions necessàries i suficients per desigualtats isocapacitàries de tipus Sobolev, i la millora de l’autointegrabilitat de les funcions de Lipschitz.
Khanfar, Abeer. "Multiple Solutions on a Ball for a Generalized Lane Emden Equation." ScholarWorks@UNO, 2008. http://scholarworks.uno.edu/td/901.
Full textOrtiz, Vargas Walter Andrés. "Sobolev inequalities: isoperimetry and symmetrization." Doctoral thesis, Universitat Autònoma de Barcelona, 2019. http://hdl.handle.net/10803/669904.
Full textMENEGATTI, GIORGIO. "Sobolev classes and bounded variation functions on domains of Wiener spaces, and applications." Doctoral thesis, Università degli studi di Ferrara, 2018. http://hdl.handle.net/11392/2488305.
Full textL’argomento principale di questo lavoro sono le funzioni a variazione limitata (BV) in spazi di Wiener astratti (un argomento di analisi infinito-dimensionale). Nella prima parte di questo lavoro, presentiamo alcuni risultati noti, e introduciamo i concetti di spazi di Wiener, di classi di Sobolev su spazi di Wiener, di funzioni BV (e insiemi di perimetro finito) in spazi di Wiener, e di funzioni BV in sottoinsiemi convessi di Spazi di Wiener (seguendo la definizione in V. I. Bogachev, A. Y. Pilipenko, A. V. Shaposhnikov, “Sobolev Functions on Infinite-dimensional domains”, J. Math. Anal. Appl., 2014); inoltre, introduciamo la teoria delle tracce su sottoinsiemi di uno spazio di Wiener( seguendo P. Celada, A. Lunardi, “Traces of Sobolev functions on regular surfaces in infinite dimensions”, J. Funct. Anal., 2014), e il concetto di convergenza di Mosco. Nella seconda parte presentiamo alcuni risultati originali. Nel capitolo 6, consideriamo un sottoinsieme O di uno spazio di Wiener che soddisfa a una condizione di regolarità, e proviamo che una funzione in W^{1,2} (O) ha traccia nulla se e solo se è il limite di una sequenza di funzioni con supporto contenuto in O. Il capitolo principale è il 7, che è dedicato all'estensione all'ambito degli spazi di Wiener di un risultato dato nella sezione 8 di (V. Barbu, M. Röckner, “Stochastic variational inequalities and applications to the total variation flow perturbed by linear multiplicative noise”, Arch. Ration. Mech. Anal., 2013): se O è un insieme convesso limitato con frontiera regolare in R^{d} e L è l'operatore di Laplace in O con condizione al bordo di Dirichlet nulla, allora il risolvente normalizzato di L è contrattivo nel senso L^1 rispetto al gradiente. Estendiamo questo risultato al caso di L operatore di Ornstein-Uhlenbeck in O con condizione al bordo di Dirichlet nulla, con misura gaussiana (usando i risultati del Capitolo 6): in questo caso O deve soddisfare una condizione (che chiamiamo convessità Gaussiana) che nel caso gaussiano prende il posto della convessità. Inoltre, estendiamo il risultato anche al caso di: L operatore di Laplace in un insieme aperto e convesso O con condizione al bordo di Neumann nulla, con misura di Lebesgue; L operatore in un insieme aperto e convesso O con condizione al bordo di Neumann nulla, con misura gaussiana. Nell'ultima parte del Capitolo 7, usiamo i precedenti risultati per dare una definizione alternativa di funzione BV in O (nel caso L^2(O) ). Nel Capitolo 8, sia X l'insieme delle funzioni continue in R^d su [ 0,1 ] con punti di partenza nell’origine fornito della misura indotta dal moto browniano con punto di partenza nell’origine; è uno spazio di Wiener. Per ogni A sottoinsieme di X, definiamo Ξ_A, insieme delle funzioni in X con immagine in A. In (M. Hino, H. Uchida, “Reflecting Ornstein–Uhlenbeck processes on pinned path spaces”, Res. Inst. Math. Sci. (RIMS), 2008) viene dimostrato che, se d ≥ 2 e A è un insieme aperto in R^d che soddisfa una condizione di uniforme palla esterna, allora Ξ_A ha perimetro finito nel senso della misura gaussiana. Presentiamo una condizione più debole su A (in dimensione sufficientemente grande) tale che Ξ_A ha perimetro finito: in particolare, A può essere il complementare di un cono convesso illimitato simmetrico.
Arden, Greg. "Approximation properties of subdivision surfaces /." Thesis, Connect to this title online; UW restricted, 2001. http://hdl.handle.net/1773/5765.
Full textSantiago, Landerson Bezerra. "O nÃcleo do calor em uma variedade riemanniana." Universidade Federal do CearÃ, 2011. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=5674.
Full textIn a connected and compact Riemannian Manifold we will introduce the concept of spectre of Laplace operator. Using the existence and unicity of the heat kernel in Riemannian manifold we proof the Hodge composition theorem. This theorem states that the Hilbert space L2(M, g) decompose in direct sum of subspaces with finite dimesion, where each subspace is the eigen-space relative of a eigenvalue of the laplacian. Furthermore, the eigenvalues form a nonnegative sequence the accumulate only in the infinity. After that we begin the construction of the heat kernel and, finally, we show that two isospetral Riemannian manifolds have the same volume.
Mahavier, William Ted. "A Numerical Method for Solving Singular Differential Equations Utilizing Steepest Descent in Weighted Sobolev Spaces." Thesis, University of North Texas, 1995. https://digital.library.unt.edu/ark:/67531/metadc278653/.
Full textTami, Abdelkader. "Etude d'un problème pour le bilaplacien dans une famille d'ouverts du plan." Thesis, Aix-Marseille, 2016. http://www.theses.fr/2016AIXM4362/document.
Full textIn this work, we study the family of problems Δ 2uω = fω with boundary conditionuω = Δ uω = 0. There, the second member is assumed to depend smoothly on ω in L2(ω), where ω = {(r, θ); 0 < r < 1, 0 < θ < ω} , 0 < ω ≤ π, is a family of truncated sectors of the plane. If ω < π it is known from Blum et Rannacher (1980) that the solution uω decomposes as uω = u1,ω + u2,ω + u3,ω, (1) where u1,ω, u2,ω are singular and u3,ω is regular. Indeed, near the origin, u1,ω(resp. u2,ω, u3,ω) is of regularity H1+πω−ǫ (resp. H2+πω−ǫ, H4) for every Q > 0, while the solution uπ is, in the neighborhood of the origin again, of regularity H4. One clearly sees a resolution of the singularity near the angle π whose descriptionis the main objective of this work. The obtained result is that there exists a decomposition (1) of uω which is uniform with respect to ω, when ω → π, with the best possible topologies for each term, and which term by term convergestowards the Taylor expansion of uπ near 0
Oliveira, Andrielber da Silva. "Metodos de interpolação real e espaços de Sobolev e Besov sobre a esfera Sd." [s.n.], 2006. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306560.
Full textDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
Made available in DSpace on 2018-08-06T13:07:08Z (GMT). No. of bitstreams: 1 Oliveira_AndrielberdaSilva_M.pdf: 1284065 bytes, checksum: 0117263cf98921db674e49f5f57d460d (MD5) Previous issue date: 2006
Resumo: O objetivo da dissertação é realizar um estudo dos espaços de Besov sobre a esfera unitária d-dimensional real Sd. No primeiro capítulo são estudados espaços de interpolação utilizando dois métodos de interpolação real. Em particular são estudados os Teoremas de Equivalência e de Reiteração para os J-método e K-método. No segundo capítulo é realizado um estudo rápido sobre análise harmônica na esfera Sd, incluindo um estudo sobre harmônicos esféricos, harmônicos zonais, somas de Cesàro e sobre um teorema de multiplicadores. O terceiro e último capítulo é o mais importante e nele são aplicados os resultados dos capítulos anteriores. São introduzidos os espaços de Besov, decompondo uma função suave definida sobre a esfera d-dimensional, em uma série de harmônicos esféricos e usando uma seqüência de polinômios zonais que podem ser vistos como uma generalização natural dos polinômios de Vallée Poussin definidos sobre o círculo unitário. O principal resultado estudado diz que todo espaço de Besov pode ser obtido como espaço de interpolação de dois espaços de Sobolev
Abstract: The purpose of this work is to make a study about Besov¿s spaces on the unit d-dimensional real sphere Sd. In the first chapter are studied spaces of interpolation using two real interpolation methods. In particular, are studied The Equivalence Theorem and The Reiteration Theorem for the J-method and the K-method. In the second chapter it is made a short study about harmonic analysis on the sphere Sd, including a study about spherics harmonics, zonal harmonics, Cesàro sums and about a multiplier theorem. The third and last chapter is the most important of this work. In this chapter are applied the results of the others chapters. Are introduced the Besov spaces, decomposing a smooth function defined on the d-dimensional sphere, in a series of harmonics spherics and using a sequence o zonal polynomials which can be seen as a natural generalization of the Vallée Poussin polynomials defined on the unit circle. The main result studied says that every Besov¿s space can be got as a interpolation space of two Sobolev¿s spaces
Mestrado
Mestre em Matemática
Bruder, Andrea S. Littlejohn Lance L. "Applied left-definite theory the Jacobi polynomials, their Sobolev orthogonality, and self-adjoint operators /." Waco, Tex. : Baylor University, 2009. http://hdl.handle.net/2104/5327.
Full textSubscript in abstract: n and n=0 in {Pn([alpha],[beta])(x)} [infinity] n=0, [mu] in (f,g)[mu], and R in [integral]Rfgd[mu]. Superscript in abstract: ([alpha],[beta]) and [infinity] in {Pn([alpha],[beta])(x)} [infinity] n=0. Includes bibliographical references (p. 115-119).
Brewster, Kevin. "Surface to surface changes of variables and applications." Diss., Columbia, Mo. : University of Missouri-Columbia, 2008. http://hdl.handle.net/10355/5759.
Full textThe entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on August 25, 2008) Vita. Includes bibliographical references.
Bento, Antonio Jorge Gomes. "Interpolation, measures of non-compactness, entropy numbers and s-numbers." Thesis, University of Sussex, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.344067.
Full textBihun, Oksana Chicone Carmen Charles. "Approximate isometries and distortion energy functionals." Diss., Columbia, Mo. : University of Missouri--Columbia, 2009. http://hdl.handle.net/10355/6129.
Full textAlgervik, Robert. "Embedding Theorems for Mixed Norm Spaces and Applications." Licentiate thesis, Karlstad : Faculty of Technology and Science, Mathematics, Karlstads universitet, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-2874.
Full textSloane, Craig Andrew. "Hardy-Sobolev-Maz'ya inequalities for fractional integrals on halfspaces and convex domains." Diss., Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/41125.
Full textBandyopadhyay, Jogia. "Optimal concentration for SU(1,1) coherent state transforms and an analogue of the Lieb-Wehrl conjecture for SU(1,1)." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/24801.
Full textCommittee Chair: Eric A. Carlen; Committee Member: Jean Bellissard; Committee Member: Michael Loss; Committee Member: Predrag Cvitanovic.
McCabe, Terence W. (Terence William). "Minimization of a Nonlinear Elasticity Functional Using Steepest Descent." Thesis, University of North Texas, 1988. https://digital.library.unt.edu/ark:/67531/metadc331296/.
Full textDima, Ute [Verfasser], and Arnd [Akademischer Betreuer] Rösch. "Regularization in fractional order Sobolev spaces for a parameter identification problem / Ute Dima ; Betreuer: Arnd Rösch." Duisburg, 2017. http://d-nb.info/1147681287/34.
Full textMedeiros, Luiz Adauto, and Juan Límaco. "On the Kirchhoff equation in noncylindrical domains of R." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/97270.
Full textChappa, Eduardo. "The x-ray transform of tensor fields /." Thesis, Connect to this title online; UW restricted, 2002. http://hdl.handle.net/1773/5750.
Full textBrauer, Uwe, and Lavi Karp. "Local existence of classical solutions for the Einstein-Euler system using weighted Sobolev spaces of fractional order." Universität Potsdam, 2006. http://opus.kobv.de/ubp/volltexte/2009/3017/.
Full textGonçalves, Breno Lucas da Costa. "An introduction to distribution theory, Fourier transform, Sobolev spaces and its applications to the Black-Scholes Equation." Master's thesis, Instituto Superior de Economia e Gestão, 2019. http://hdl.handle.net/10400.5/19247.
Full textA maior parte da teoria citada em cursos introdutórios de análise matemática e cálculo foi elaborada ainda antes do século XVIII. No entanto, em meados de 1950, Laurent Schwartz desenvolveu um novo conceito que mudou e redefiniu a noção de função. A definição de derivada e transformada de Fourier são dois dos conceitos mais importantes em análise e essenciais para o estudo de equações diferenciais parciais. No entanto, note-se que nem todas as funções são diferenciáveis ou possuem uma transformada de Fourier. A teoria de distribuições permite esta correção ao incorporar as funções clássicas numa classe maior de objetos matemáticos. Esta dissertação tem como objetivo completar o artigo publicado por D. da Silva, K. Igibayeva, A. Khoroshevskay e Z.Sakayevz. De modo a alcançar o nosso objectivo apresentam-se inicialmente as ferramentas necessárias para uma introdução à teoria de distribuições, transformadas de Fourier e espaços de Sobolev que serão usadas para o cálculo explícito da solução da equação do calor.
Most of the mathematical theory study in standard courses of calculus were developed even before the eighteen century. However, around the year of 1950, Laurent Schwartz came up with a new concept that would change and redefine the concept of function. Differentiability and the Fourier transform are two of the most important notions in analysis and genuinely essential when working with partial differential equations. It is well-known that not all functions are differentiable or have a Fourier transform. The theory of distributions allows us to correct this issue by embedding classical functions into a larger class of mathematical objects. This dissertation aims to complete the article published by D. Da Silva, K. Igibayeva, A. Khoroshevskay and Z.Sakayeva (2018). To accomplish our goal, we provide and develop the necessary tools for an introductory course in distribution theory, Fourier transforms, Sobolev spaces and use them to solve the heat diffusion equation.
info:eu-repo/semantics/publishedVersion
Benetti, Francesco. "The Cauchy problem for the wave equation." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/18369/.
Full textRoth, John Charles. "Perturbations of Kähler-Einstein metrics /." Thesis, Connect to this title online; UW restricted, 1999. http://hdl.handle.net/1773/5737.
Full textAlgervik, Robert. "Embedding Theorems for Mixed Norm Spaces and Applications." Doctoral thesis, Karlstads universitet, Avdelningen för matematik, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-5646.
Full textMontealegre, Scott Juan. "Initial value problem for a coupled system of Kadomtsev-Petviashvili II equations in Sobolev spaces of negative indices." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/95255.
Full textMantegazza, Carlo. "Smooth geometric evolutions of hypersurfaces and singular approximation of mean curvature flow." Doctoral thesis, Scuola Normale Superiore, 2014. http://hdl.handle.net/11384/85686.
Full text