Lectures On Elliptic Partial Differential Equations

Author : Luigi Ambrosio,Alessandro Carlotto,Annalisa Massaccesi
Publisher : Springer
Page : 230 pages
File Size : 43,7 Mb
Release : 2019-01-10
Category : Mathematics
ISBN : 9788876426513

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Lectures on Elliptic Partial Differential Equations by Luigi Ambrosio,Alessandro Carlotto,Annalisa Massaccesi Pdf

The book originates from the Elliptic PDE course given by the first author at the Scuola Normale Superiore in recent years. It covers the most classical aspects of the theory of Elliptic Partial Differential Equations and Calculus of Variations, including also more recent developments on partial regularity for systems and the theory of viscosity solutions.

Author : Qing Han,Fanghua Lin
Publisher : American Mathematical Soc.
Page : 161 pages
File Size : 44,5 Mb
Release : 2011
Category : Differential equations, Elliptic
ISBN : 9780821853139

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Elliptic Partial Differential Equations by Qing Han,Fanghua Lin Pdf

This volume is based on PDE courses given by the authors at the Courant Institute and at the University of Notre Dame, Indiana. Presented are basic methods for obtaining various a priori estimates for second-order equations of elliptic type with particular emphasis on maximal principles, Harnack inequalities, and their applications. The equations considered in the book are linear; however, the presented methods also apply to nonlinear problems.

Author : Nikolaĭ Vladimirovich Krylov
Publisher : American Mathematical Soc.
Page : 164 pages
File Size : 54,9 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821805695

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Lectures on Elliptic and Parabolic Equations in Hölder Spaces by Nikolaĭ Vladimirovich Krylov Pdf

These lectures concentrate on fundamentals of the modern theory of linear elliptic and parabolic equations in H older spaces. Krylov shows that this theory - including some issues of the theory of nonlinear equations - is based on some general and extremely powerful ideas and some simple computations. The main object of study is the first boundary-value problems for elliptic and parabolic equations, with some guidelines concerning other boundary-value problems such as the Neumann or oblique derivative problems or problems involving higher-order elliptic operators acting on the boundary. Numerical approximations are also discussed. This book, containing 200 exercises, aims to provide a good understanding of what kind of results are available and what kinds of techniques are used to obtain them.

Author : I. G. Petrovsky
Publisher : Courier Corporation
Page : 261 pages
File Size : 43,9 Mb
Release : 2012-12-13
Category : Mathematics
ISBN : 9780486155081

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Lectures on Partial Differential Equations by I. G. Petrovsky Pdf

Graduate-level exposition by noted Russian mathematician offers rigorous, readable coverage of classification of equations, hyperbolic equations, elliptic equations, and parabolic equations. Translated from the Russian by A. Shenitzer.

Author : David Gilbarg
Publisher : Unknown
Page : 266 pages
File Size : 49,7 Mb
Release : 1958
Category : Differential equations, Partial
ISBN : STANFORD:36105025508024

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Lectures on Elliptic Partial Differential Equations by David Gilbarg Pdf

Author : Nikolaĭ Vladimirovich Krylov
Publisher : American Mathematical Soc.
Page : 377 pages
File Size : 54,7 Mb
Release : 2008
Category : Differential equations, Elliptic
ISBN : 9780821846841

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Lectures on Elliptic and Parabolic Equations in Sobolev Spaces by Nikolaĭ Vladimirovich Krylov Pdf

This book concentrates on the basic facts and ideas of the modern theory of linear elliptic and parabolic equations in Sobolev spaces. The main areas covered in this book are the first boundary-value problem for elliptic equations and the Cauchy problem for parabolic equations. In addition, other boundary-value problems such as the Neumann or oblique derivative problems are briefly covered. As is natural for a textbook, the main emphasis is on organizing well-known ideas in a self-contained exposition. Among the topics included that are not usually covered in a textbook are a relatively recent development concerning equations with $\textsf{VMO}$ coefficients and the study of parabolic equations with coefficients measurable only with respect to the time variable. There are numerous exercises which help the reader better understand the material. After going through the book, the reader will have a good understanding of results available in the modern theory of partial differential equations and the technique used to obtain them. Prerequesites are basics of measure theory, the theory of $L p$ spaces, and the Fourier transform.

Author : Grigoriĭ Ilʹich Eskin
Publisher : American Mathematical Soc.
Page : 432 pages
File Size : 44,5 Mb
Release : 2011
Category : Differential equations, Elliptic
ISBN : 9780821852842

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Lectures on Linear Partial Differential Equations by Grigoriĭ Ilʹich Eskin Pdf

This is a reader-friendly, relatively short introduction to the modern theory of linear partial differential equations. An effort has been made to present complete proofs in an accessible and self-contained form. The first three chapters are on elementary distribution theory and Sobolev spaces. The following chapters study the Cauchy problem for parabolic and hyperbolic equations, boundary value problems for elliptic equations, heat trace asymptotics, and scattering theory.

Author : David Gilbarg,Neil S. Trudinger
Publisher : Springer Science & Business Media
Page : 544 pages
File Size : 54,8 Mb
Release : 2001-01-12
Category : Mathematics
ISBN : 3540411607

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Elliptic Partial Differential Equations of Second Order by David Gilbarg,Neil S. Trudinger Pdf

This work aims to be of interest to those who have to work with differential equations and acts either as a reference or as a book to learn from. The authors have made the treatment self-contained.

Author : Jacques-Louis Lions,B. Singbal
Publisher : Unknown
Page : 296 pages
File Size : 42,8 Mb
Release : 1957
Category : Differential equations
ISBN : UOM:39015017331201

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Lectures on Elliptic Partial Differential Equations by Jacques-Louis Lions,B. Singbal Pdf

Author : Lipman Bers,Fritz John,Martin Schechter
Publisher : American Mathematical Soc.
Page : 372 pages
File Size : 46,5 Mb
Release : 1964-12-31
Category : Differential equations, Partial
ISBN : 0821896989

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Partial Differential Equations by Lipman Bers,Fritz John,Martin Schechter Pdf

This book consists of two main parts. The first part, "Hyperbolic and Parabolic Equations", written by F. John, contains a well-chosen assortment of material intended to give an understanding of some problems and techniques involving hyperbolic and parabolic equations. The emphasis is on illustrating the subject without attempting to survey it. The point of view is classical, and this serves well in furnishing insight into the subject; it also makes it possible for the lectures to be read by someone familiar with only the fundamentals of real and complex analysis. The second part, "Elliptic Equations", written by L. Bers and M. Schechter, contains a very readable account of the results and methods of the theory of linear elliptic equations, including the maximum principle, Hilbert-space methods, and potential-theoretic methods. It also contains a brief discussion of some quasi-linear elliptic equations. The book is suitable for graduate students and researchers interested in partial differential equations.

Author : E.W. Stredulinsky
Publisher : Springer
Page : 149 pages
File Size : 41,9 Mb
Release : 2006-12-08
Category : Mathematics
ISBN : 9783540389286

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Weighted Inequalities and Degenerate Elliptic Partial Differential Equations by E.W. Stredulinsky Pdf

Author : Donald Greenspan
Publisher : Prentice Hall
Page : 208 pages
File Size : 52,7 Mb
Release : 1968
Category : Boundary value problems
ISBN : UOM:39015001317042

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Lectures on the Numerical Solution of Linear, Singular, and Nonlinear Differential Equations by Donald Greenspan Pdf

Author : D. Gilbarg,N. S. Trudinger
Publisher : Springer Science & Business Media
Page : 409 pages
File Size : 52,5 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783642963797

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Elliptic Partial Differential Equations of Second Order by D. Gilbarg,N. S. Trudinger Pdf

This volume is intended as an essentially self contained exposition of portions of the theory of second order quasilinear elliptic partial differential equations, with emphasis on the Dirichlet problem in bounded domains. It grew out of lecture notes for graduate courses by the authors at Stanford University, the final material extending well beyond the scope of these courses. By including preparatory chapters on topics such as potential theory and functional analysis, we have attempted to make the work accessible to a broad spectrum of readers. Above all, we hope the readers of this book will gain an appreciation of the multitude of ingenious barehanded techniques that have been developed in the study of elliptic equations and have become part of the repertoire of analysis. Many individuals have assisted us during the evolution of this work over the past several years. In particular, we are grateful for the valuable discussions with L. M. Simon and his contributions in Sections 15.4 to 15.8; for the helpful comments and corrections of J. M. Cross, A. S. Geue, J. Nash, P. Trudinger and B. Turkington; for the contributions of G. Williams in Section 10.5 and of A. S. Geue in Section 10.6; and for the impeccably typed manuscript which resulted from the dedicated efforts oflsolde Field at Stanford and Anna Zalucki at Canberra. The research of the authors connected with this volume was supported in part by the National Science Foundation.

Author : David Gilbarg,Neil S. Trudinger
Publisher : Springer
Page : 544 pages
File Size : 46,7 Mb
Release : 1983
Category : Mathematics
ISBN : UCSD:31822026147728

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Elliptic Partial Differential Equations of Second Order by David Gilbarg,Neil S. Trudinger Pdf

From the reviews: "This is a book of interest to any having to work with differential equations, either as a reference or as a book to learn from. The authors have taken trouble to make the treatment self-contained. It (is) suitable required reading for a PhD student. Although the material has been developed from lectures at Stanford, it has developed into an almost systematic coverage that is much longer than could be covered in a year's lectures". Newsletter, New Zealand Mathematical Society, 1985 "Primarily addressed to graduate students this elegant book is accessible and useful to a broad spectrum of applied mathematicians". Revue Roumaine de Mathématiques Pures et Appliquées,1985

Author : Lipman Bers,Fritz John,Martin Schechter
Publisher : American Mathematical Soc.
Page : 370 pages
File Size : 51,7 Mb
Release : 1964
Category : Differential equations, Partial
ISBN : 9780821800492

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Partial Differential Equations by Lipman Bers,Fritz John,Martin Schechter Pdf

Divided in two main parts, this title contains an assortment of material intended to give an understanding of some problems and techniques involving hyperbolic and parabolic equations. Suitable for graduate students and researchers interested in partial differential equations, it also includes a discussion of some quasi-linear elliptic equations.