*Accepted Paper*

**Inserted:** 8 oct 2001

**Last Updated:** 13 dec 2002

**Journal:** Asymptotic Analysis

**Year:** 2001

**Abstract:**

In this paper we give a result of $G$-convergence for a class of strongly degenerate parabolic equations in the case of periodic coefficients. The operators have the form $\mu (x) {\partial }_t - %%%{\displaystyle {{\partial }\over{\partial t}}} - {\rm div}(a(x,t) \cdot D)$ where the quadratic form associated to $a(x,t)$ is degenerating as a Muckenhoupt weight and the coefficient $\mu$ is greater or equal to zero, possibly $\mu \equiv 0$, that is the operator may be elliptic, parabolic or elliptic-parabolic.

**Keywords:**
G-convergence, homgenization, equations in divergence form

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