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arXiv:0810.0522 [math.AP]AbstractReferencesReviewsResources

Boundary estimates for positive solutions to second order elliptic equations

Mikhail V. Safonov

Published 2008-10-02Version 2

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.

Comments: 20 pages, 23 references
Categories: math.AP
Subjects: 35J15, 35J67, 35B05
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