Elliptic Differential Equations And Obstacle Problems
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Elliptic Differential Equations And Obstacle Problems
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Author : Giovanni Maria Troianiello
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Elliptic Differential Equations And Obstacle Problems written by Giovanni Maria Troianiello 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 2013-11-11 with Mathematics categories.
In the few years since their appearance in the mid-sixties, variational inequalities have developed to such an extent and so thoroughly that they may now be considered an "institutional" development of the theory of differential equations (with appreciable feedback as will be shown). This book was written in the light of these considerations both in regard to the choice of topics and to their treatment. In short, roughly speaking my intention was to write a book on second-order elliptic operators, with the first half of the book, as might be expected, dedicated to function spaces and to linear theory whereas the second, nonlinear half would deal with variational inequalities and non variational obstacle problems, rather than, for example, with quasilinear or fully nonlinear equations (with a few exceptions to which I shall return later). This approach has led me to omit any mention of "physical" motivations in the wide sense of the term, in spite of their historical and continuing importance in the development of variational inequalities. I here addressed myself to a potential reader more or less aware of the significant role of variational inequalities in numerous fields of applied mathematics who could use an analytic presentation of the fundamental theory, which would be as general and self-contained as possible.
Fine Regularity Of Solutions Of Elliptic Partial Differential Equations
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Author : Jan Malý
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Fine Regularity Of Solutions Of Elliptic Partial Differential Equations written by Jan Malý 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 1997 with Mathematics categories.
The primary objective of this monograph is to give a comprehensive exposition of results surrounding the work of the authors concerning boundary regularity of weak solutions of second order elliptic quasilinear equations in divergence form. The book also contains a complete development of regularity of solutions of variational inequalities, including the double obstacle problem, where the obstacles are allowed to be discontinuous. The book concludes with a chapter devoted to the existence theory thus providing the reader with a complete treatment of the subject ranging from regularity of weak solutions to the existence of weak solutions.
Nonlinear Partial Differential Equations And Free Boundaries Elliptic Equations
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Author : J. I. Díaz
language : en
Publisher:
Release Date : 1985
Nonlinear Partial Differential Equations And Free Boundaries Elliptic Equations written by J. I. Díaz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Boundary value problems categories.
In this Research Note the author brings together the body of known work and presents many recent results relating to nonlinear partial differential equations that give rise to a free boundary--usually the boundary of the set where the solution vanishes identically. The formation of such a boundary depends on an adequate balance between two of the terms of the equation that represent the particular characteristics of the phenomenon under consideration: diffusion, absorption, convection, evolution etc. These balances do not occur in the case of a linear equation or an arbitrary nonlinear equation. Their characterization is studied for several classes of nonlinear equations relating to applications such as chemical reactions, non-Newtonian fluids, flow through porous media and biological populations. In this first volume, the free boundary for nonlinear elliptic equations is discussed. A second volume dealing with parabolic and hyperbolic equations is in preparation.
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
Progress In Partial Differential Equations
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Author : Catherine Bandle
language : en
Publisher: Chapman & Hall/CRC
Release Date : 1992
Progress In Partial Differential Equations written by Catherine Bandle and has been published by Chapman & Hall/CRC this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
Regularity Estimates For Nonlinear Elliptic And Parabolic Problems
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Author : John Lewis
language : en
Publisher: Springer
Release Date : 2012-03-02
Regularity Estimates For Nonlinear Elliptic And Parabolic Problems written by John Lewis and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-02 with Mathematics categories.
The issue of regularity has played a central role in the theory of Partial Differential Equations almost since its inception, and despite the tremendous advances made it still remains a very fruitful research field. In particular considerable strides have been made in regularity estimates for degenerate and singular elliptic and parabolic equations over the last several years, and in many unexpected and challenging directions. Because of all these recent results, it seemed high time to create an overview that would highlight emerging trends and issues in this fascinating research topic in a proper and effective way. The course aimed to show the deep connections between these topics and to open new research directions through the contributions of leading experts in all of these fields.
Integro Differential Elliptic Equations
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Author : Xavier Fernández-Real
language : en
Publisher: Springer Nature
Release Date :
Integro Differential Elliptic Equations written by Xavier Fernández-Real and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Nonlinear Partial Differential Equations For Future Applications
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Author : Shigeaki Koike
language : en
Publisher: Springer Nature
Release Date : 2021-04-16
Nonlinear Partial Differential Equations For Future Applications written by Shigeaki Koike and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-16 with Mathematics categories.
This volume features selected, original, and peer-reviewed papers on topics from a series of workshops on Nonlinear Partial Differential Equations for Future Applications that were held in 2017 at Tohoku University in Japan. The contributions address an abstract maximal regularity with applications to parabolic equations, stability, and bifurcation for viscous compressible Navier–Stokes equations, new estimates for a compressible Gross–Pitaevskii–Navier–Stokes system, singular limits for the Keller–Segel system in critical spaces, the dynamic programming principle for stochastic optimal control, two kinds of regularity machineries for elliptic obstacle problems, and new insight on topology of nodal sets of high-energy eigenfunctions of the Laplacian. This book aims to exhibit various theories and methods that appear in the study of nonlinear partial differential equations.
Global Bifurcation In Variational Inequalities
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Author : Vy Khoi Le
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Global Bifurcation In Variational Inequalities written by Vy Khoi Le 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 2013-12-01 with Mathematics categories.
An up-to-date and unified treatment of bifurcation theory for variational inequalities in reflexive spaces and the use of the theory in a variety of applications, such as: obstacle problems from elasticity theory, unilateral problems; torsion problems; equations from fluid mechanics and quasilinear elliptic partial differential equations. The tools employed are those of modern nonlinear analysis. Accessible to graduate students and researchers who work in nonlinear analysis, nonlinear partial differential equations, and additional research disciplines that use nonlinear mathematics.
Obstacle Problems In Mathematical Physics
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Author : J.-F. Rodrigues
language : en
Publisher: Elsevier
Release Date : 1987-03-01
Obstacle Problems In Mathematical Physics written by J.-F. Rodrigues and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-03-01 with Science categories.
The aim of this research monograph is to present a general account of the applicability of elliptic variational inequalities to the important class of free boundary problems of obstacle type from a unifying point of view of classical Mathematical Physics. The first part of the volume introduces some obstacle type problems which can be reduced to variational inequalities. Part II presents some of the main aspects of the theory of elliptic variational inequalities, from the abstract hilbertian framework to the smoothness of the variational solution, discussing in general the properties of the free boundary and including some results on the obstacle Plateau problem. The last part examines the application to free boundary problems, namely the lubrication-cavitation problem, the elastoplastic problem, the Signorini (or the boundary obstacle) problem, the dam problem, the continuous casting problem, the electrochemical machining problem and the problem of the flow with wake in a channel past a profile.