*Published Paper*

**Inserted:** 15 dec 2001

**Last Updated:** 18 jan 2002

**Journal:** J. of Convex Analysis

**Volume:** 8

**Number:** 2

**Year:** 2001

**Abstract:**

In this paper we study the convergence of the Cauchy-Dirichlet problems
for a sequence of parabolic operators
$\Par_h = \la_h {{\partial}\over{\partial t}} -
{\rm div} ( a_h(x,t) \cdot D)$ where the matrices of the coefficients
$a_h(x,t)$ verify the following degenerate elliptic condition
$$
\la_{h}(x)

\xi^{2} \leq ( a_{{h}}(x,t) \cdot \xi, \xi )
\leq L \la_{h}(x)

\xi^{2,
}
$$
being $(\la_h)_h$ a sequence of weights satisfying a uniform Muckenhoupt's
condition in $h$.
When $a_h=a_h(x)$ we compare this result with the analogous results
for the sequence of operators
$A_h = - {\rm div} ( a_h(x) \cdot D)$ and
${\cal Q}_h = {{\partial}\over{\partial t}} - {\rm div} ( a_h(x) \cdot D)$

**Keywords:**
G-convergence, operators in divergence form, Muckenhoupt weights