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The obstacle problem (Publications of the Scuola Normale Superiore)

by Luis A. Caffarelli

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ISBN

:

9788876422492
Publisher

:

Edizioni della Normale
Subject

:

Mathematics
Binding

:

PAPERBACK
Pages

:

54
Year

:

2007

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~~4435.0~~

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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.

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