TY  - JOUR
A1  - Abatangelo, Nicola
A1  - Jarohs, Sven
A1  - Saldaña de Fuentes, Alberto
T1  - Fractional Laplacians on ellipsoids
T2  - Mathematics in engineering
N2  - 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.
KW  - positivity preserving property
KW  - torsion function
KW  - point inversion
Y1  - 2020
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/81958
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-819583
SN  - 2640-3501
VL  - 3
IS  - 5
SP  - 1
EP  - 34
PB  - AIMS Press
CY  - Springfield, MO
ER  -