Calculus of Variations and Geometric Measure Theory

F. Paronetto

Some new results on the convergence of degenerate elliptic and parabolic equations

created on 15 Dec 2001
modified on 18 Jan 2002


Published Paper

Inserted: 15 dec 2001
Last Updated: 18 jan 2002

Journal: J. of Convex Analysis
Volume: 8
Number: 2
Year: 2001


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 $$ \lah(x)
2 \leq ( a{h}(x,t) \cdot \xi, \xi ) \leq L \lah(x)
2, $$ 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