Asymptotic Behaviour of Relaxed Dirichiet Problems Involving a Dirichlet-Poincar Form

Abstract

We study the convergence of the solutions of a sequence of relaxed Dirichlet prob lems relative to Dirichlet forms to the solution of the Γ-limit problem. In particular we prove the strong convergence in $D^P_0[a,Ω](1≤p≤2)$ and the existence of "correctors" for the strong convergence in $D0[a,Ω]$. The above two results are generalizations to our framework of previous results proved in [10] in the usual uniformly elliptic setting.