TITLE

Uniqueness results for quasilinear parabolic equations through viscosity solutions' methods

AUTHOR(S)
Guy Barles; Samuel Biton; Mariane Bourgoing; Olivier Ley
PUB. DATE
October 2003
SOURCE
Calculus of Variations & Partial Differential Equations;Oct2003, Vol. 18 Issue 2, p159
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
In this article, we are interested in uniqueness results for viscosity solutions of a general class of quasilinear, possibly degenerate, parabolic equations set in ${\mathbb R}^N$ . Using classical viscosity solutions' methods, we obtain a general comparison result for solutions with polynomial growths but with a restriction on the growth of the initial data. The main application is the uniqueness of solutions for the mean curvature equation for graphs which was only known in the class of uniformly continuous functions. An application to the mean curvature flow is given.
ACCESSION #
11090215

 

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