Holes with Dirichlet Conditions

Abstract

In the fall of 1975, after studying the homogenization of monotone operators, described in Chap. 11, and the question of correctors, described in Chap. 13, I thought about degenerate elliptic problems, corresponding to holes in the domain, imposing either Dirichlet boundary conditions, described in this Chap. 15, or Neumann boundary conditions, described in Chap. 16. I started with the case of a homogeneous Dirichlet condition on the boundaries of the holes, which I discarded after proving easily that the solutions converge to 0, by an argument about the constant in the Poincaré inequality.