Boundary estimates for positive solutions to second order elliptic equations

Mikhail V. Safonov

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arXiv · 0810.0522

Boundary estimates for positive solutions to second order elliptic equations

Mikhail V. Safonov

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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.

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Mikhail V. Safonov. 2008-10-02. Boundary estimates for positive solutions to second order elliptic equations. https://arxiv.org/abs/0810.0522

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