The Obstacle Problem (Publications of the Scuola Normale Superiore)

The Obstacle Problem (Publications of the Scuola Normale Superiore)

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  • 製本 Paperback:紙装版/ペーパーバック版／ページ数 54 p.
  • 言語 ENG
  • 商品コード 9788876422492
  • DDC分類 515

Full Description


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.