Estimates of Solutions and Asymptotic Symmetry for Parabolic Equations on Bounded Domains
Author: Poláčik, Peter
Source: Archive for Rational Mechanics and Analysis, Volume 183, Number 1, January 2007 , pp. 59-91(33)
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.
Document Type: Research Article
Affiliations: Email: email@example.com
Publication date: January 1, 2007