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- W3026552620 abstract "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 $sin(1,sqrt{3}+3/2)$ in any dimension $ngeq 2$. 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." @default.
- W3026552620 created "2020-05-29" @default.
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- W3026552620 date "2020-05-19" @default.
- W3026552620 modified "2023-09-27" @default.
- W3026552620 title "Fractional Laplacians on ellipsoids" @default.
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