Hopf's lemma for a class of singular/degenerate PDE-s

Hayk Mikayelyan; Henrik Shahgholian

Hopf's lemma for a class of singular/degenerate PDE-s

Analysis of PDEs 2014-03-03 v1

Authors: Hayk Mikayelyan , Henrik Shahgholian

Abstract

This paper concerns Hopf's boundary point lemma, in certain $C^{1,Dini}$ -type domains, for a class of singular/degenerate PDE-s, including $p$ -Laplacian. Using geometric properties of levels sets for harmonic functions in convex rings, we construct sub-solutions to our equations that play the role of a barrier from below. By comparison principle we then conclude Hopf's lemma.

Keywords

hopf's lemma singular pde degenerate pde p-laplacian boundary point lemma sub-solutions comparison principle

Cite

@article{arxiv.1402.7157,
  title  = {Hopf's lemma for a class of singular/degenerate PDE-s},
  author = {Hayk Mikayelyan and Henrik Shahgholian},
  journal= {arXiv preprint arXiv:1402.7157},
  year   = {2014}
}

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