A Saint-Venant type principle for Dirichlet forms on discontinuous media

Abstract

We consider certain families of Dirichlet forms of diffusion type that describe the variational behaviour of possibly highly nonhomogeneous and nonisotropic bodies and we prove a structural Harnack inequality and Saint Venant type energy decays for their local solution. Estimates for the Green functions are also considered. © 1995 Fondazione Annali di Matematica Pura ed Applicata.