Boundary estimates for positive solutions to second order elliptic equations
Abstract
Description
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.
20 pages, 23 references
20 pages, 23 references