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arXiv · 1402.7157

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

Hayk Mikayelyan·Henrik Shahgholian
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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.

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Hayk Mikayelyan, Henrik Shahgholian. 2014-02-28. Hopf's lemma for a class of singular/degenerate PDE-s. https://arxiv.org/abs/1402.7157

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