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The obstacle problem

1999-10-01 Mathematics
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Release : 1999-10-01
Genre : Mathematics
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Book Rating : 492/5 ( reviews)

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Book Synopsis The obstacle problem by : Luis Angel Caffarelli

Download or read book The obstacle problem written by Luis Angel Caffarelli. This book was released on 1999-10-01. Available in PDF, EPUB and Kindle. Book excerpt: 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

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 661/5 ( reviews)

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Book Synopsis European Congress of Mathematics by : Carles Casacuberta

Download or read book European Congress of Mathematics written by Carles Casacuberta. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: 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

1987-03-01 Mathematics
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Release : 1987-03-01
Genre : Mathematics
Kind : eBook
Book Rating : 45X/5 ( reviews)

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Book Synopsis Obstacle Problems in Mathematical Physics by : J.-F. Rodrigues

Download or read book Obstacle Problems in Mathematical Physics written by J.-F. Rodrigues. This book was released on 1987-03-01. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Random Obstacle Problems

2017-02-27 Mathematics
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Release : 2017-02-27
Genre : Mathematics
Kind : eBook
Book Rating : 962/5 ( reviews)

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Book Synopsis Random Obstacle Problems by : Lorenzo Zambotti

Download or read book Random Obstacle Problems written by Lorenzo Zambotti. This book was released on 2017-02-27. Available in PDF, EPUB and Kindle. Book excerpt: Studying the fine properties of solutions to Stochastic (Partial) Differential Equations with reflection at a boundary, this book begins with a discussion of classical one-dimensional diffusions as the reflecting Brownian motion, devoting a chapter to Bessel processes, and moves on to function-valued solutions to SPDEs. Inspired by the classical stochastic calculus for diffusions, which is unfortunately still unavailable in infinite dimensions, it uses integration by parts formulae on convex sets of paths in order to describe the behaviour of the solutions at the boundary and the contact set between the solution and the obstacle. The text may serve as an introduction to space-time white noise, SPDEs and monotone gradient systems. Numerous open research problems in both classical and new topics are proposed.

Elliptic Differential Equations and Obstacle Problems

2013-11-11 Mathematics
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Release : 2013-11-11
Genre : Mathematics
Kind : eBook
Book Rating : 149/5 ( reviews)

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Book Synopsis Elliptic Differential Equations and Obstacle Problems by : Giovanni Maria Troianiello

Download or read book Elliptic Differential Equations and Obstacle Problems written by Giovanni Maria Troianiello. This book was released on 2013-11-11. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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