
Journal of Convex Analysis 09 (2002), No. 1, 031054 Copyright Heldermann Verlag 2002 Some New Results on the Convergence of Degenerate Elliptic and Parabolic Equations Fabio Paronetto Dip. di Matematica, Universitą di Lecce, Via Annesano, 73100 Lecce, Italy fabio.paronetto@unile.it We consider a sequence of matrices a_{h}(x,t) whose minimum eigenvalue is a positive function λ_{h}(x) and the maximum one is Lλ_{h}(x), λ_{h} satisfying a uniform Muckenhoupt's condition. We study Gconvergence of the sequence of linear parabolic operators in divergence form associated to these matrices and with coefficient λ_{h} in front of the temporal derivative. When the matrices are depending only on the variable x we compare this result with the analogous results for the sequence of elliptic operators and the sequence of standard parabolic operators associated to the same sequence of matrices. Keywords: Jumping problems, variational inequalities, nonsmooth critical point theory. MSC: 35D05; 58J05 [ Fulltextpdf (592 KB)] 