Boundary estimates for positive solutions to second order elliptic equations
Analysis of PDEs
2008-10-03 v2
Abstract
Consider positive solutions to second order elliptic equations with measurable coefficients in a bounded domain, which vanish on a portion of the boundary. We give simple necessary and sufficient geometric conditions on the domain, which guarantee the Hopf-Oleinik type estimates and the boundary Lipschitz estimates for solutions. These conditions are sharp even for harmonic functions.
Cite
@article{arxiv.0810.0522,
title = {Boundary estimates for positive solutions to second order elliptic equations},
author = {Mikhail V. Safonov},
journal= {arXiv preprint arXiv:0810.0522},
year = {2008}
}
Comments
20 pages, 23 references