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 : 1987-07-31

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 1987-07-31 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.

Direct Methods In The Calculus Of Variations

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Author : Enrico Giusti
language : en
Publisher: World Scientific
Release Date : 2003

Direct Methods In The Calculus Of Variations written by Enrico Giusti and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.

This book provides a comprehensive discussion on the existence and regularity of minima of regular integrals in the calculus of variations and of solutions to elliptic partial differential equations and systems of the second order. While direct methods for the existence of solutions are well known and have been widely used in the last century, the regularity of the minima was always obtained by means of the Euler equation as a part of the general theory of partial differential equations. In this book, using the notion of the quasi-minimum introduced by Giaquinta and the author, the direct methods are extended to the regularity of the minima of functionals in the calculus of variations, and of solutions to partial differential equations. This unified treatment offers a substantial economy in the assumptions, and permits a deeper understanding of the nature of the regularity and singularities of the solutions. The book is essentially self-contained, and requires only a general knowledge of the elements of Lebesgue integration theory.

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 Mathematics 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.

Asymptotic Issues For Some Partial Differential Equations

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Author : Michel Marie Chipot
language : en
Publisher: World Scientific
Release Date : 2016-06-14

Asymptotic Issues For Some Partial Differential Equations written by Michel Marie Chipot and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-14 with Mathematics categories.

Much progress has been made in recent years on the issue of asymptotic behavior of problems set in cylinders. This book goes one step further by presenting the latest accomplishments on asymptotic behavior in domains which become unbounded.It also investigates new issues which have emerged including existence and uniqueness of solution in unbounded domains, anisotropic singular perturbations, periodic behavior forced by periodic data. These new advances are treated with original techniques developed to investigate the asymptotic behavior of various problems.Theories investigated throughout the book can be applied to other problems related to partial differential equations, making it an important text for students and researchers within the discipline.Asymptotic Issues for Some Partial Differential Equations is an updated account of ℓ Goes to Plus Infinity, published by Birkhäuser in 2002.

Analysis And Topology In Nonlinear Differential Equations

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Author : Djairo G de Figueiredo
language : en
Publisher: Springer
Release Date : 2014-06-16

Analysis And Topology In Nonlinear Differential Equations written by Djairo G de Figueiredo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-16 with Mathematics categories.

This volume is a collection of articles presented at the Workshop for Nonlinear Analysis held in João Pessoa, Brazil, in September 2012. The influence of Bernhard Ruf, to whom this volume is dedicated on the occasion of his 60th birthday, is perceptible throughout the collection by the choice of themes and techniques. The many contributors consider modern topics in the calculus of variations, topological methods and regularity analysis, together with novel applications of partial differential equations. In keeping with the tradition of the workshop, emphasis is given to elliptic operators inserted in different contexts, both theoretical and applied. Topics include semi-linear and fully nonlinear equations and systems with different nonlinearities, at sub- and supercritical exponents, with spectral interactions of Ambrosetti-Prodi type. Also treated are analytic aspects as well as applications such as diffusion problems in mathematical genetics and finance and evolution equations related to electromechanical devices.

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.

The Obstacle Problem

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Author : Luis Angel Caffarelli
language : en
Publisher: Edizioni della Normale
Release Date : 1999-10-01

The Obstacle Problem written by Luis Angel Caffarelli and has been published by Edizioni della Normale this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-10-01 with Mathematics categories.

The material presented here corresponds to Fermi lectures that I was invited to deliver at the Scuola Normale di Pisa in the spring of 1998. The obstacle problem consists in studying the properties of minimizers of the Dirichlet integral in a domain D of Rn, among all those configurations u with prescribed boundary values and costrained to remain in D above a prescribed obstacle F. In the Hilbert space H1(D) of all those functions with square integrable gradient, we consider the closed convex set K of functions u with fixed boundary value and which are greater than F in D. There is a unique point in K minimizing the Dirichlet integral. That is called the solution to the obstacle problem.

Global Bifurcation In Variational Inequalities

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Author : Vy Khoi Le
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-01-24

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 1997-01-24 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.

Nonlinear Differential Problems With Smooth And Nonsmooth Constraints

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Author : Dumitru Motreanu
language : en
Publisher: Academic Press
Release Date : 2018-02-05

Nonlinear Differential Problems With Smooth And Nonsmooth Constraints written by Dumitru Motreanu and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-05 with Mathematics categories.

Nonlinear Differential Problems with Smooth and Nonsmooth Constraints systematically evaluates how to solve boundary value problems with smooth and nonsmooth constraints. Primarily covering nonlinear elliptic eigenvalue problems and quasilinear elliptic problems using techniques amalgamated from a range of sophisticated nonlinear analysis domains, the work is suitable for PhD and other early career researchers seeking solutions to nonlinear differential equations. Although an advanced work, the book is self-contained, requiring only graduate-level knowledge of functional analysis and topology. Whenever suitable, open problems are stated and partial solutions proposed. The work is accompanied by end-of-chapter problems and carefully curated references. - Builds from functional analysis and operator theory, to nonlinear elliptic systems and control problems - Outlines the evolution of the main ideas of nonlinear analysis and their roots in classical mathematics - Presented with numerous end-of-chapter exercises and sophisticated open problems - Illustrated with pertinent industrial and engineering numerical examples and applications - Accompanied by hundreds of curated references, saving readers hours of research in conducting literature analysis

Nonsmooth Variational Problems And Their Inequalities

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Author : Siegfried Carl
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-07

Nonsmooth Variational Problems And Their Inequalities written by Siegfried Carl 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 2007-06-07 with Mathematics categories.

This monograph focuses primarily on nonsmooth variational problems that arise from boundary value problems with nonsmooth data and/or nonsmooth constraints, such as multivalued elliptic problems, variational inequalities, hemivariational inequalities, and their corresponding evolution problems. It provides a systematic and unified exposition of comparison principles based on a suitably extended sub-supersolution method.