A Hopf lemma for the regional fractional Laplacian
- We provide a Hopf boundary lemma for the regional fractional Laplacian (−Δ)sΩ, with Ω ⊂ RN a bounded open set. More precisely, given u a pointwise or weak super-solution of the equation (−Δ)s u = c(x)u in Ω, we show that the ratio u(x)∕(dist(x, 𝜕Ω))2s−1 is strictly Ω positive as x approaches the boundary 𝜕Ω of Ω. We also prove a strong maximum principle for distributional super-solutions.
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| Author: | Nicola AbatangeloORCiD, Mouhamed Moustapha Fall, Remi Yvant TemgouaORCiDGND |
|---|---|
| URN: | urn:nbn:de:hebis:30:3-694543 |
| DOI: | https://doi.org/10.1007/s10231-022-01234-6 |
| ISSN: | 1618-1891 |
| Parent Title (English): | Annali di matematica pura ed applicata |
| Publisher: | Springer |
| Place of publication: | Berlin ; Heidelberg [u.a.] |
| Document Type: | Article |
| Language: | English |
| Date of Publication (online): | 2022/06/20 |
| Date of first Publication: | 2022/06/20 |
| Publishing Institution: | Universitätsbibliothek Johann Christian Senckenberg |
| Release Date: | 2023/06/02 |
| Tag: | Distributional super-solution; Hopf boundary lemma; Pointwise super-solution; Regional fractional Laplacian; Weak super-solution |
| Volume: | 100.2022 |
| Issue: | Early View: Online Version before inclusion in an issue |
| Page Number: | 19 |
| Note: | Early View: Online Version before inclusion in an issue. |
| Note: | Open access funding provided by Alma Mater Studiorum - Università di Bologna within the CRUI-CARE Agreement. |
| Institutes: | Informatik und Mathematik |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Sammlungen: | Universitätspublikationen |
| Licence (German): |  Creative Commons - CC BY - Namensnennung 4.0 International |
