A comparison principle for a sobolev gradient semi-flow

Timothy Blass, Rafael De La Llave, Enrico Valdinoci

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We consider gradient descent equations for energy functionals of the type S(u) = 1 2 hu(x);A(x)u(x)iL2 +R V (x; u) dx, where A is a uniformly elliptic operator of order 2, with smooth coeffcients. The gradient descent equation for such a functional depends on the metric under consideration. We consider the steepest descent equation for S where the gradient is an element of the Sobolev space H,β β ε(0; 1), with a metric that depends on A and a positive number γ β sup jV22j. We prove a weak comparison principle for such a gradient ow.

Original languageEnglish
Pages (from-to)69-91
Number of pages23
JournalCommunications on Pure and Applied Analysis
Volume10
Issue number1
DOIs
Publication statusPublished - 1 Jan 2011
Externally publishedYes

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