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math.AP2020
An elliptic boundary value problem with fractional nonlinearity
Nicola Abatangelo, Matteo Cozzi
We investigate existence and uniqueness of solutions to second-order elliptic boundary value problems containing a power nonlinearity applied to a fractional Laplacian. We detect t…
math.AP2020
Fractional Laplacians on ellipsoids
Nicola Abatangelo, Sven Jarohs, Alberto Saldaña
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 expre…