Analysis & PDE

  • Anal. PDE
  • Volume 9, Number 2 (2016), 439-458.

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

Darya E. Apushkinskaya and Alexander I. Nazarov

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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.

Article information

Anal. PDE, Volume 9, Number 2 (2016), 439-458.

Received: 2 April 2015
Revised: 29 September 2015
Accepted: 16 December 2015
First available in Project Euclid: 16 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J15: Second-order elliptic equations 35B45: A priori estimates

elliptic equations Hopf–Oleinik lemma Dini continuity counterexample


Apushkinskaya, Darya E.; Nazarov, Alexander I. A counterexample to the Hopf–Oleinik lemma (elliptic case). Anal. PDE 9 (2016), no. 2, 439--458. doi:10.2140/apde.2016.9.439.

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