$\Gamma$-convergence for Strongly Local Dirichlet Forms in Open Sets with Holes

We consider homogenization problems with holes for strongly local Dirichlet forms in the cases of the Dirichlet and Neumann homogeneous conditions on the boundaries of the holes. In the second case, the main difficulties arise from the absence of a group structure on the underlying space and from the nonperiodic distribution of the holes. Complete proofs of the results will appear later.