The obstacle problem
Luis A. Caffarelli
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.
Категорії:
Рік:
1998
Видавництво:
Pisa
Мова:
english
Сторінки:
56
ISBN 10:
8876422498
ISBN 13:
9788876422492
Серії:
Publications of the Scuola Normale Superiore
Файл:
DJVU, 294 KB
IPFS:
,
english, 1998