Estimates of solutions and asymptotic symmetry for parabolic equations on bounded domains

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

We consider fully nonlinear parabolic equations on bounded domains under Dirichlet boundary conditions. Assuming that the equation and the domain satisfy certain symmetry conditions, we prove that each bounded positive solution of the Dirichlet problem is asymptotically symmetric. Compared with previous results of this type, we do not assume certain crucial hypotheses, such as uniform (with respect to time) positivity of the solution or regularity of the nonlinearity in time. Our method is based on estimates of solutions of linear parabolic problems, in particular on a theorem on asymptotic positivity of such solutions.

Original languageEnglish (US)
Pages (from-to)59-91
Number of pages33
JournalArchive For Rational Mechanics And Analysis
Volume183
Issue number1
DOIs
StatePublished - Jan 1 2007

Fingerprint Dive into the research topics of 'Estimates of solutions and asymptotic symmetry for parabolic equations on bounded domains'. Together they form a unique fingerprint.

Cite this