Elliptic Differential Equations
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Elliptic Partial Differential Equations Of Second Order
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Author : David Gilbarg
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-01-12
Elliptic Partial Differential Equations Of Second Order written by David Gilbarg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-12 with Mathematics categories.
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.
Elliptic Differential Equations
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Author : W. Hackbusch
language : en
Publisher: Springer Science & Business Media
Release Date : 1992
Elliptic Differential Equations written by W. Hackbusch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Language Arts & Disciplines categories.
Derived from a lecture series for college mathematics students, introduces the methods of dealing with elliptical boundary-value problems--both the theory and the numerical analysis. Includes exercises. Translated and somewhat expanded from the 1987 German version. Annotation copyright by Book News, Inc., Portland, OR
Elliptic Equations An Introductory Course
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Author : Michel Chipot
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-02-19
Elliptic Equations An Introductory Course written by Michel Chipot and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-19 with Mathematics categories.
The aim of this book is to introduce the reader to different topics of the theory of elliptic partial differential equations by avoiding technicalities and refinements. Apart from the basic theory of equations in divergence form it includes subjects such as singular perturbation problems, homogenization, computations, asymptotic behaviour of problems in cylinders, elliptic systems, nonlinear problems, regularity theory, Navier-Stokes system, p-Laplace equation. Just a minimum on Sobolev spaces has been introduced, and work or integration on the boundary has been carefully avoided to keep the reader's attention on the beauty and variety of these issues. The chapters are relatively independent of each other and can be read or taught separately. Numerous results presented here are original and have not been published elsewhere. The book will be of interest to graduate students and faculty members specializing in partial differential equations.
Elliptic Differential Equations
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Author : Wolfgang Hackbusch
language : en
Publisher: Springer
Release Date : 2017-06-01
Elliptic Differential Equations written by Wolfgang Hackbusch and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-01 with Mathematics categories.
This book simultaneously presents the theory and the numerical treatment of elliptic boundary value problems, since an understanding of the theory is necessary for the numerical analysis of the discretisation. It first discusses the Laplace equation and its finite difference discretisation before addressing the general linear differential equation of second order. The variational formulation together with the necessary background from functional analysis provides the basis for the Galerkin and finite-element methods, which are explored in detail. A more advanced chapter leads the reader to the theory of regularity. Individual chapters are devoted to singularly perturbed as well as to elliptic eigenvalue problems. The book also presents the Stokes problem and its discretisation as an example of a saddle-point problem taking into account its relevance to applications in fluid dynamics.
Lectures On Elliptic Partial Differential Equations
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Author : Luigi Ambrosio
language : en
Publisher: Springer
Release Date : 2019-01-10
Lectures On Elliptic Partial Differential Equations written by Luigi Ambrosio and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-10 with Mathematics categories.
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.
Elliptic Partial Differential Equations
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Author : Qing Han
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
Elliptic Partial Differential Equations written by Qing Han and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
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.
Elliptic Partial Differential Equations Of Second Order
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Author : D. Gilbarg
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Elliptic Partial Differential Equations Of Second Order written by D. Gilbarg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
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.
Stable Solutions Of Elliptic Partial Differential Equations
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Author : Louis Dupaigne
language : en
Publisher: CRC Press
Release Date : 2011-03-15
Stable Solutions Of Elliptic Partial Differential Equations written by Louis Dupaigne and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-15 with Mathematics categories.
Stable solutions are ubiquitous in differential equations. They represent meaningful solutions from a physical point of view and appear in many applications, including mathematical physics (combustion, phase transition theory) and geometry (minimal surfaces). Stable Solutions of Elliptic Partial Differential Equations offers a self-contained presentation of the notion of stability in elliptic partial differential equations (PDEs). The central questions of regularity and classification of stable solutions are treated at length. Specialists will find a summary of the most recent developments of the theory, such as nonlocal and higher-order equations. For beginners, the book walks you through the fine versions of the maximum principle, the standard regularity theory for linear elliptic equations, and the fundamental functional inequalities commonly used in this field. The text also includes two additional topics: the inverse-square potential and some background material on submanifolds of Euclidean space.
Partial Differential Equations Of Elliptic Type
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Author : C. Miranda
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Partial Differential Equations Of Elliptic Type written by C. Miranda and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
In the theory of partial differential equations, the study of elliptic equations occupies a preeminent position, both because of the importance which it assumes for various questions in mathematical physics, and because of the completeness of the results obtained up to the present time. In spite of this, even in the more classical treatises on analysis the theory of elliptic equations has been considered and illustrated only from particular points of view, while the only expositions of the whole theory, the extremely valuable ones by LICHTENSTEIN and AscoLI, have the charac ter of encyclopedia articles and date back to many years ago. Consequently it seemed to me that it would be of some interest to try to give an up-to-date picture of the present state of research in this area in a monograph which, without attaining the dimensions of a treatise, would nevertheless be sufficiently extensive to allow the expo sition, in some cases in summary form, of the various techniques used in the study of these equations.
Second Order Elliptic Equations And Elliptic Systems
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Author : Ya-Zhe Chen
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Second Order Elliptic Equations And Elliptic Systems written by Ya-Zhe Chen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
There are two parts to the book. In the first part, a complete introduction of various kinds of a priori estimate methods for the Dirichlet problem of second order elliptic partial differential equations is presented. In the second part, the existence and regularity theories of the Dirichlet problem for linear and nonlinear second order elliptic partial differential systems are introduced. The book features appropriate materials and is an excellent textbook for graduate students. The volume is also useful as a reference source for undergraduate mathematics majors, graduate students, professors, and scientists.