#### Vol. 9, No. 2, 2016

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

### Darya E. Apushkinskaya and Alexander I. Nazarov

Vol. 9 (2016), No. 2, 439–458
##### Abstract

We construct a new counterexample to the Hopf–Oleinik boundary point lemma. It shows that for convex domains, the ${C}^{1,Dini}$ assumption on $\partial \Omega$ is the necessary and sufficient condition providing the estimates of Hopf–Oleinik type.

 Dedicated to Professor M.V. Safonov
##### Keywords
elliptic equations, Hopf–Oleinik lemma, Dini continuity, counterexample
##### Mathematical Subject Classification 2010
Primary: 35J15, 35B45