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The obstacle problem

Publications of the Scuola Normale Superiore

By (author) Luis Angel Caffarelli
Format: Paperback
Publisher: Birkhauser Verlag AG, Pisa, Italy
Imprint: Scuola Normale Superiore
Published: 1st Oct 1999
Dimensions: w 170mm h 240mm d 5mm
Weight: 168g
ISBN-10: 8876422498
ISBN-13: 9788876422492
Barcode No: 9788876422492
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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