Dirichlet problems in domains bounded by thin layers with random thickness (Q1114510)

We investigate the asymptotic behaviour of sequences \((F_ h)\) of random functionals which are associated with Dirichlet problems in domains surrounded by thin layers with random thickness. By means of capacitary approach, a compactness result for sequences \((F_ h)\) is given. More specifically, under suitable assumptions on \((F_ h)\), we prove that there exists a subsequence \((F_{\sigma (h)})\) converging in probability to a deterministic random functional F. Also a meaningful characterization of the limit functional F is obtained. An example is considered.