On the loss of maximum principles for higher-order fractional Laplacians
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- by Nicola Abatangelo, Sven Jarohs and Alberto Saldaña PDF
- Proc. Amer. Math. Soc. 146 (2018), 4823-4835 Request permission
Abstract:
We study the existence and positivity of solutions to problems involving higher-order fractional Laplacians $(-\Delta )^s$ for any $s>1$. In particular, using a suitable variational framework and the nonlocal properties of these operators, we provide an explicit counterexample to general maximum principles for $s\in (n,n+1)$ with $n\in \mathbb N$ odd, and we mention some particular domains where positivity preserving properties do hold.References
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Additional Information
- Nicola Abatangelo
- Affiliation: Département de Mathḿatiques, Université Libre de Bruxelles CP 214, boulevard du Triomphe, 1050 Ixelles, Belgium
- MR Author ID: 1069950
- Email: nicola.abatangelo@ulb.ac.be
- Sven Jarohs
- Affiliation: Institut für Mathematik, Goethe-Universität, Frankfurt, Robert-Mayer-Straße 10, 60054 Frankfurt am Main, Germany
- MR Author ID: 1055972
- Email: jarohs@math.uni-frankfurt.de
- Alberto Saldaña
- Affiliation: Institut für Analysis, Karlsruhe Institute for Technology, Englerstraße 2, 76131, Karlsruhe, Germany
- ORCID: 0000-0002-4134-0082
- Email: alberto.saldana@partner.kit.edu
- Received by editor(s): March 6, 2018
- Published electronically: August 8, 2018
- Communicated by: Svitlana Mayboroda
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 4823-4835
- MSC (2010): Primary 35B50; Secondary 35S15, 35J35
- DOI: https://doi.org/10.1090/proc/14165
- MathSciNet review: 3856149