Calculus of Variations and Geometric Measure Theory
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F. Paronetto

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

created on 15 Dec 2001
modified on 18 Jan 2002

[BibTeX]

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

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