Wiener's criterion and Γ-convergence

Dirichlet problems with homogeneous boundary conditions in (possibly irregular) domains and stationary Schrödinger equations with (possibly singular) nonnegative potentials are considered as special cases of more general equations of the form −Δu + µu = 0, whereµ is an arbitrary given nonnegative Borel measure in ℝn. The stability and compactness of weak solutions under suitable variational perturbations ofµ is investigated and stable pointwise estimates for the modulus of continuity and the “energy” of local solutions are obtained.

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