Fractional Laplacians on ellipsoids
- We show explicit formulas for the evaluation of (possibly higher-order) fractional Laplacians (-△)ˢ of some functions supported on ellipsoids. In particular, we derive the explicit expression of the torsion function and give examples of s-harmonic functions. As an application, we infer that the weak maximum principle fails in eccentric ellipsoids for s ∈ (1; √3 + 3/2) in any dimension n ≥ 2. We build a counterexample in terms of the torsion function times a polynomial of degree 2. Using point inversion transformations, it follows that a variety of bounded and unbounded domains do not satisfy positivity preserving properties either and we give some examples.
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| Author: | Nicola AbatangeloORCiD, Sven JarohsORCiDGND, Alberto Saldaña de FuentesORCiDGND |
|---|---|
| URN: | urn:nbn:de:hebis:30:3-819583 |
| DOI: | https://doi.org/10.3934/mine.2021038 |
| ISSN: | 2640-3501 |
| Parent Title (English): | Mathematics in engineering |
| Publisher: | AIMS Press |
| Place of publication: | Springfield, MO |
| Document Type: | Article |
| Language: | English |
| Date of Publication (online): | 2020/09/22 |
| Date of first Publication: | 2020/09/22 |
| Publishing Institution: | Universitätsbibliothek Johann Christian Senckenberg |
| Release Date: | 2024/03/11 |
| Tag: | point inversion; positivity preserving property; torsion function |
| Volume: | 3 |
| Issue: | 5 |
| Page Number: | 34 |
| First Page: | 1 |
| Last Page: | 34 |
| 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 |
