Submitted Paper

Inserted: 5 mar 2003

Year: 2003

Abstract:

In this paper we prove $C^{1,\alpha}$-regularity (near flat points) of the free boundary $\partial\{u>0\}\cap\Omega$ in the Alt-Caffarelli type minimum problem for the $p$-Laplace operator: $$ J(u)=\int_\Omega\left(
\nabla u
^p + \lambda^p\chi_{{\{u>0\}}\right)dx\rightarrow} \min\qquad (1<p<\infty.) $$

Download:

• pmin.pdf