Calculus of Variations and Geometric Measure Theory

F. Paronetto

Homogenization of degenerate elliptic-parabolic equations

created on 08 Oct 2001
modified on 13 Dec 2002


Accepted Paper

Inserted: 8 oct 2001
Last Updated: 13 dec 2002

Journal: Asymptotic Analysis
Year: 2001


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