Wiener's Criterion And Г-Convergence

Institute For Mathematics And Its Applications, University of Minnesota - 1985, 80 pages.In this paper we can find description of a class of equations, the relaxed Dirichlet problems, and a variational convergence for their perturbation, the $\gamma$-convergence, with two main requirements in mind.One one hand, this of problem and this convergence must be general enough to include the asymptotic limits that naturally occur in the perturbed problems mentioned at the beginning. On the other hand, they should be specific enough to allow stable behavior of the solutions at certain privileged points of the domain.As to the first point, we will be able to prove compactness as well as density properties. As to second one, we will establish a stable variational Wiener's criterion for regularity and we will also obtain stable estimates at an arbitrary point of the domain.