Filtern
Erscheinungsjahr
- 2020 (1)
Dokumenttyp
Sprache
- Englisch (1)
Volltext vorhanden
- ja (1)
Gehört zur Bibliographie
- nein (1)
Schlagworte
Institut
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.