TY - JOUR
T1 - Estimates of solutions and asymptotic symmetry for parabolic equations on bounded domains
AU - Polacik, Peter
PY - 2007/1/1
Y1 - 2007/1/1
N2 - 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.
AB - 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.
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U2 - 10.1007/s00205-006-0004-x
DO - 10.1007/s00205-006-0004-x
M3 - Article
AN - SCOPUS:33750167250
SN - 0003-9527
VL - 183
SP - 59
EP - 91
JO - Archive For Rational Mechanics And Analysis
JF - Archive For Rational Mechanics And Analysis
IS - 1
ER -