On the asymptotic behavior of Dirichlet problems in a riemannian manifold less small random holes

$P_{h}$ {ll -div (|Duh|p-2 Duh)=g, & in D Eh uhH1,p0(D Eh). . 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 $(P_{h})$ , characterizing the limit problem for suitable sequences of random sets.

Double layer potentials and the Dirichlet problem

Ivan Netuka (1974)

Czechoslovak Mathematical Journal

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An analytic approach to semiclassical potential theory

S. Kwapień (1969)

Studia Mathematica

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