Fractional Laplacians on ellipsoids
| Autor: | Alberto Saldaña, Sven Jarohs, Nicola Abatangelo |
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| Přispěvatelé: | Abatangelo N., Jarohs S., Saldana A. |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Polynomial Degree (graph theory) Applied Mathematics lcsh:T57-57.97 35R11 35B50 35G15 35C05 35S15 Dimension (graph theory) Function (mathematics) Maximum principle Mathematics - Analysis of PDEs Bounded function torsion function lcsh:Applied mathematics. Quantitative methods Torsion (algebra) FOS: Mathematics positivity preserving property point inversion Mathematical Physics Analysis Counterexample Mathematics Analysis of PDEs (math.AP) |
| Zdroj: | Mathematics in Engineering, Vol 3, Iss 5, Pp 1-34 (2021) |
| Popis: | We show explicit formulas for the evaluation of (possibly higher-order) fractional Laplacians 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 and we give some examples. 6 pictures, 27 pages |
| Databáze: | OpenAIRE |
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