A fractional Hopf Lemma for sign-changing solutions

In this paper we prove some results on the boundary behavior of solutions to fractional elliptic problems. Firstly, we establish a Hopf Lemma for solutions to some integro-differential equations. The main novelty of our result is that we do not assume any global condition on the sign of the solution...

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Published inCommunications in partial differential equations Vol. 49; no. 3; pp. 217 - 241
Main Authors Dipierro, Serena, Soave, Nicola, Valdinoci, Enrico
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 03.03.2024
Taylor & Francis Ltd
Subjects
Differential equations
Hopf Lemma
nonlocal equations
qualitative behavior
zeros of solutions
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ISSN0360-5302
1532-4133
DOI10.1080/03605302.2024.2337637

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Summary:In this paper we prove some results on the boundary behavior of solutions to fractional elliptic problems. Firstly, we establish a Hopf Lemma for solutions to some integro-differential equations. The main novelty of our result is that we do not assume any global condition on the sign of the solutions. Secondly, we show that non-trivial radial solutions cannot have infinitely many zeros accumulating at the boundary. We provide concrete examples to show that the results obtained are sharp.
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ISSN:0360-5302
1532-4133
DOI:10.1080/03605302.2024.2337637