Elliptic Differential Equations and Obstacle Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Elliptic Differential Equations and Obstacle Problems write by Giovanni Maria Troianiello. This book was released on 2013-11-11. Elliptic Differential Equations and Obstacle Problems available in PDF, EPUB and Kindle. 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
Fine Regularity of Solutions of Elliptic Partial Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Fine Regularity of Solutions of Elliptic Partial Differential Equations write by Jan Malý. This book was released on 1997. Fine Regularity of Solutions of Elliptic Partial Differential Equations available in PDF, EPUB and Kindle. 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
Nonlinear Partial Differential Equations and Free Boundaries: Elliptic equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonlinear Partial Differential Equations and Free Boundaries: Elliptic equations write by J. I. Díaz. This book was released on 1985. Nonlinear Partial Differential Equations and Free Boundaries: Elliptic equations available in PDF, EPUB and Kindle. 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 Equations: An Introductory Course
Elliptic Equations: An Introductory Course - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Elliptic Equations: An Introductory Course write by Michel Chipot. This book was released on 2009-02-19. Elliptic Equations: An Introductory Course available in PDF, EPUB and Kindle. 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.
The obstacle problem
The obstacle problem - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The obstacle problem write by Luis Angel Caffarelli. This book was released on 1999-10-01. The obstacle problem available in PDF, EPUB and Kindle. 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.
