A counterexample to the Hopf-Oleinik lemma (elliptic case)

Abstract

We construct a new counterexample confirming the sharpness of the Dini-type condition for the boundary of $\Omega$. In particular, we show that for convex domains the Dini-type assumption is the necessary and sufficient condition which guarantees the Hopf-Oleinik type estimates.

26 pages, 1 figure

References in corpus (1)

• Boundary estimates for positive solutions to second order elliptic equations

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