An optimal Liouville theorem for the linear heat equation with a nonlinear boundary condition
Analysis of PDEs
2020-09-30 v1
Abstract
Liouville theorems for scaling invariant nonlinear parabolic problems in the whole space and/or the halfspace (saying that the problem does not posses positive bounded solutions defined for all times ) guarantee optimal estimates of solutions of related initial-boundary value problems in general domains. We prove an optimal Liouville theorem for the linear equation in the halfspace complemented by the nonlinear boundary condition , .
Keywords
Cite
@article{arxiv.2009.13923,
title = {An optimal Liouville theorem for the linear heat equation with a nonlinear boundary condition},
author = {Pavol Quittner},
journal= {arXiv preprint arXiv:2009.13923},
year = {2020}
}