Mosco-convergence and Wiener measures for conductive thin boundaries

The Mosco-convergence of energy functionals and the convergence of associated Wiener measures are proved for a domain with highly conductive thin boundary. We obtain those results for matrix-valued conductivities and a family of speed measures (measures of the underlying domain). In particular, this family includes the Lebesgue measure and the one which makes the energy functional superposition. The expectation of the displacement of the associated processes close to the boundary goes to +∞ due to the explosion of the conductivity at the limit.