SOME CASES OF HOMOGENIZATION OF LINEARLY COERCIVE GRADIENT CONSTRAINED VARIATIONAL PROBLEMS

Abstract

A homogenization problem for integral functionals defined on Lipschitz functions verifying pointwise oscillating constraints on the gradient is studied in the case in which the constraint takes only the values 0 and +∞. Such situation is of interest in some problems in electrostatics and elastic-plastic torsion theory. An integral representation result on BV-spaces for the “homogenized functional”, and convergence results for minimum values and solutions of Dirichlet and Neumann problems, are proved without assuming any geometrical condition on the set of the zeroes of the constraint and under mild assumptions on the integrands. An application to a concrete problem in electrostatics is also given.