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

We consider a sequence of matrices $a_h(x,t)$ whose minimum eigenvalue is a positive function $\lambda_h(x)$ and the maximum one is $L\lambda_h(x)$, $\lambda_h$ 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 $\lambda_h$ 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.