On the convergence of a class of degenerate parabolic equations

Abstract

In this paper we study the convergence of the Cauchy-Dirichlet problems for a sequence of parabolic operators P h = ∂ ∂t − div (a h(x,t) · D) , where the matrices of the coefficient a h ( x, t) verify the following degenerate elliptic condition: λ h(x)|ζ| 2≤ (a h(x,t)⋯ζ,ζ)≤Lλ h(x)|ζ| 2, being ( λ h ) h a sequence of weights satisfying an uniform Muckenhoupt's condition in h.