Some New Results on the Convergence of Degenerate Elliptic and Parabolic Equations

We consider a sequence of matrices ah(x,t) whose minimum eigenvalue is a positive function λh(x) and the maximum one is Lλh(x), λh satisfying a uniform Muckenhoupt's condition. We study G-convergence of the sequence of linear parabolic operators in divergence form associated to these matrices and with coefficient λh 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.