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.
European Congress of Mathematics
European Congress of Mathematics - 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 European Congress of Mathematics write by Carles Casacuberta. This book was released on 2012-12-06. European Congress of Mathematics available in PDF, EPUB and Kindle. This is the second volume of the proceedings of the third European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, the list of lectures, and short summaries of the achievements of the prize winners as well as papers by plenary and parallel speakers. The second volume collects articles by prize winners and speakers of the mini-symposia. This two-volume set thus gives an overview of the state of the art in many fields of mathematics and is therefore of interest to every professional mathematician.
Obstacle Problems in Mathematical Physics
Obstacle Problems in Mathematical Physics - 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 Obstacle Problems in Mathematical Physics write by J.-F. Rodrigues. This book was released on 1987-03-01. Obstacle Problems in Mathematical Physics available in PDF, EPUB and Kindle. 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.
Elliptic Differential Equations and Obstacle Problems
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.
Regularity of Free Boundaries in Obstacle-Type Problems
Regularity of Free Boundaries in Obstacle-Type 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 Regularity of Free Boundaries in Obstacle-Type Problems write by Arshak Petrosyan. This book was released on 2012. Regularity of Free Boundaries in Obstacle-Type Problems available in PDF, EPUB and Kindle. The regularity theory of free boundaries flourished during the late 1970s and early 1980s and had a major impact in several areas of mathematics, mathematical physics, and industrial mathematics, as well as in applications. Since then the theory continued to evolve. Numerous new ideas, techniques, and methods have been developed, and challenging new problems in applications have arisen. The main intention of the authors of this book is to give a coherent introduction to the study of the regularity properties of free boundaries for a particular type of problems, known as obstacle-type problems. The emphasis is on the methods developed in the past two decades. The topics include optimal regularity, nondegeneracy, rescalings and blowups, classification of global solutions, several types of monotonicity formulas, Lipschitz, $C^1$, as well as higher regularity of the free boundary, structure of the singular set, touch of the free and fixed boundaries, and more. The book is based on lecture notes for the courses and mini-courses given by the authors at various locations and should be accessible to advanced graduate students and researchers in analysis and partial differential equations.
