| Autor: |
Nicola Abatangelo, Sven Jarohs, Alberto Saldaña |
| Jazyk: |
angličtina |
| Rok vydání: |
2021 |
| Předmět: |
|
| Zdroj: |
Mathematics in Engineering, Vol 3, Iss 5, Pp 1-34 (2021) |
| Druh dokumentu: |
article |
| ISSN: |
2640-3501 |
| DOI: |
10.3934/mine.2021038?viewType=HTML |
| Popis: |
We show explicit formulas for the evaluation of (possibly higher-order) fractional Laplacians~$\Ds$ 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~$s\in(1,\sqrt{3}+3/2)$ in any dimension~$n\geq 2$. 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. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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