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

D. E. Apushkinskaya; A. I. Nazarov

doi:10.2140/apde.2016.9.439

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

Analysis of PDEs 2017-03-21 v2

Authors: D. E. Apushkinskaya , A. I. Nazarov

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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.

Keywords

hopf-oleinik lemma dini condition elliptic equations convex domains boundary estimates counterexample

Cite

@article{arxiv.1503.02179,
  title  = {A counterexample to the Hopf-Oleinik lemma (elliptic case)},
  author = {D. E. Apushkinskaya and A. I. Nazarov},
  journal= {arXiv preprint arXiv:1503.02179},
  year   = {2017}
}

Comments

26 pages, 1 figure

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