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 C1,Dini assumption on Ω 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
Milestones
Received: 2 April 2015
Revised: 29 September 2015
Accepted: 16 December 2015
Published: 24 March 2016
Authors
Darya E. Apushkinskaya
Department of Mathematics
Saarland University
P.O. Box 151150
Saarbrücken 66041
Germany
St. Petersburg State University
7/9 Universitetskaya nab.
St. Petersburg 199034
Russia
Alexander I. Nazarov
St. Petersburg Department
Steklov Institute
Fontanka 27
St. Petersburg 191023
Russia
St. Petersburg State University
7/9 Universitetskaya nab.
St. Petersburg 199034
Russia