Introduction To Regularity Theory For Nonlinear Elliptic Systems
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Introduction To Regularity Theory For Nonlinear Elliptic Systems
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Author : Mariano Giaquinta
language : en
Publisher: Birkhauser
Release Date : 1993
Introduction To Regularity Theory For Nonlinear Elliptic Systems written by Mariano Giaquinta and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
Introduction To The Regularity Theory For Nonlinear Elliptic Systems
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Author : Mariano Giaquinta
language : en
Publisher:
Release Date : 1984
Introduction To The Regularity Theory For Nonlinear Elliptic Systems written by Mariano Giaquinta and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with categories.
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.
Introduction To The Theory Of Nonlinear Elliptic Equations
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Author : Jindric Necas
language : en
Publisher:
Release Date : 1986-12-29
Introduction To The Theory Of Nonlinear Elliptic Equations written by Jindric Necas and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-12-29 with Mathematics categories.
This book is concerned with the study of boundary value problems for nonlinear, second order, elliptic partial differential equations. A short introduction to Sobolev and Morrey-Campanato spaces and to methods of approximation is included.
Elliptic Regularity Theory
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Author : Lisa Beck
language : en
Publisher: Springer
Release Date : 2016-04-08
Elliptic Regularity Theory written by Lisa Beck and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-08 with Mathematics categories.
These lecture notes provide a self-contained introduction to regularity theory for elliptic equations and systems in divergence form. After a short review of some classical results on everywhere regularity for scalar-valued weak solutions, the presentation focuses on vector-valued weak solutions to a system of several coupled equations. In the vectorial case, weak solutions may have discontinuities and so are expected, in general, to be regular only outside of a set of measure zero. Several methods are presented concerning the proof of such partial regularity results, and optimal regularity is discussed. Finally, a short overview is given on the current state of the art concerning the size of the singular set on which discontinuities may occur. The notes are intended for graduate and postgraduate students with a solid background in functional analysis and some familiarity with partial differential equations; they will also be of interest to researchers working on related topics.
Regularity Results For Nonlinear Elliptic Systems And Applications
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Author : Alain Bensoussan
language : en
Publisher:
Release Date : 2014-01-15
Regularity Results For Nonlinear Elliptic Systems And Applications written by Alain Bensoussan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Regularity Results For Nonlinear Elliptic Systems And Applications
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Author : Alain Bensoussan
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Regularity Results For Nonlinear Elliptic Systems And Applications written by Alain Bensoussan 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 2013-04-17 with Mathematics categories.
This book collects many helpful techniques for obtaining regularity results for solutions of nonlinear systems of partial differential equations. These are applied in various cases to provide useful examples and relevant results, particularly in such fields as fluid mechanics, solid mechanics, semiconductor theory and game theory.
An Introduction To The Regularity Theory For Elliptic Systems Harmonic Maps And Minimal Graphs
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Author : Mariano Giaquinta
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-07-30
An Introduction To The Regularity Theory For Elliptic Systems Harmonic Maps And Minimal Graphs written by Mariano Giaquinta 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 2013-07-30 with Mathematics categories.
This volume deals with the regularity theory for elliptic systems. We may find the origin of such a theory in two of the problems posed by David Hilbert in his celebrated lecture delivered during the International Congress of Mathematicians in 1900 in Paris: 19th problem: Are the solutions to regular problems in the Calculus of Variations always necessarily analytic? 20th problem: does any variational problem have a solution, provided that certain assumptions regarding the given boundary conditions are satisfied, and provided that the notion of a solution is suitably extended? During the last century these two problems have generated a great deal of work, usually referred to as regularity theory, which makes this topic quite relevant in many fields and still very active for research. However, the purpose of this volume, addressed mainly to students, is much more limited. We aim to illustrate only some of the basic ideas and techniques introduced in this context, confining ourselves to important but simple situations and refraining from completeness. In fact some relevant topics are omitted. Topics include: harmonic functions, direct methods, Hilbert space methods and Sobolev spaces, energy estimates, Schauder and L^p-theory both with and without potential theory, including the Calderon-Zygmund theorem, Harnack's and De Giorgi-Moser-Nash theorems in the scalar case and partial regularity theorems in the vector valued case; energy minimizing harmonic maps and minimal graphs in codimension 1 and greater than 1. In this second deeply revised edition we also included the regularity of 2-dimensional weakly harmonic maps, the partial regularity of stationary harmonic maps, and their connections with the case p=1 of the L^p theory, including the celebrated results of Wente and of Coifman-Lions-Meyer-Semmes.
Optimization Of Elliptic Systems
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Author : Pekka Neittaanmaki
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-01-04
Optimization Of Elliptic Systems written by Pekka Neittaanmaki 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 2007-01-04 with Mathematics categories.
The present monograph is intended to provide a comprehensive and accessible introduction to the optimization of elliptic systems. This area of mathematical research, which has many important applications in science and technology. has experienced an impressive development during the past two decades. There are already many good textbooks dealing with various aspects of optimal design problems. In this regard, we refer to the works of Pironneau [1984], Haslinger and Neittaanmaki [1988], [1996], Sokolowski and Zolksio [1992], Litvinov [2000], Allaire [2001], Mohammadi and Pironneau [2001], Delfour and Zolksio [2001], and Makinen and Haslinger [2003]. Already Lions [I9681 devoted a major part of his classical monograph on the optimal control of partial differential equations to the optimization of elliptic systems. Let us also mention that even the very first known problem of the calculus of variations, the brachistochrone studied by Bernoulli back in 1696. is in fact a shape optimization problem. The natural richness of this mathematical research subject, as well as the extremely large field of possible applications, has created the unusual situation that although many important results and methods have already been est- lished, there are still pressing unsolved questions. In this monograph, we aim to address some of these open problems; as a consequence, there is only a minor overlap with the textbooks already existing in the field.
Introduction To The Theory Of Nonlinear Elliptic Equations
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Author : Jindřich Nečas
language : en
Publisher:
Release Date : 1986
Introduction To The Theory Of Nonlinear Elliptic Equations written by Jindřich Nečas and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Differential equations, Elliptic categories.