The obstacle problem
Author | : Luis Angel Caffarelli |
Publisher | : Edizioni della Normale |
Total Pages | : 0 |
Release | : 1999-10-01 |
Genre | : Mathematics |
ISBN | : 9788876422492 |
Download The obstacle problem Book 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.