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Wiener’s criterion and \(\Gamma\)-convergence. (English) Zbl 0644.35033
The authors describe a class of equations, the relaxed Dirichlet problems, and a variational convergence for their perturbations, the gamma-convergence. The relaxed Dirichlet problem is a general formulation with a potential given by a nonnegative Borel measure in \({\mathbb{R}}^ n.\) This formulation includes both the Dirichlet problems with homogeneous boundary conditions in (possibly irregular) domains and the Schrödinger equations with (possibly singular) nonnegative potentials. The stability and compactness of weak solutions under suitable variational perturbations of the potential is investigated and stable pointwise estimates for the modulus of continuity and the energy of local solutions are obtained.
Reviewer: M.Codegone

MSC:
35J25 Boundary value problems for second-order elliptic equations
35J67 Boundary values of solutions to elliptic equations and elliptic systems
49J20 Existence theories for optimal control problems involving partial differential equations
35J10 Schrödinger operator, Schrödinger equation
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