Accepted Paper

Inserted: 7 jan 2002

Journal: Boll. Un. Mat. It.
Year: 2001

Abstract:

We investigate sequences of nonlinear Dirichlet problems of the form $$ \left \{\eqalign { -& \, div(\vert Du_h \vert ^{p-2} Du_h) = g \qquad{\rm in} \,\, D\backslash E_h \cr & u_h \in H^{1,p}₀(D\backslash E_h). \cr } \right.$$ where $2\leq{p}\leq{n}$ and $E_h$ are random subsets of a bounded open set $D$ of $*R*^n$ ($n\geq 2$). By means of a variational approach, we study the asymptotic behaviour of solutions of the problems, characterizing the limit problem for suitable sequences of random sets.

Keywords: p-Laplacian, p-capacity, random set