12 papers
Oscillatory Phenomena for Higher-Order Fractional Laplacians
Nicola Abatangelo, Sven Jarohs
We collect some peculiarities of higher-order fractional Laplacians , , with special attention to the range , which show their oscillatory nature. These inc…
On the shape of the first fractional eigenfunction
Nicola Abatangelo, Sven Jarohs
We show that the first eigenfunction of the fractional Laplacian , , is superharmonic in the unitary ball up to dimension . To this aim, we also rely on…
Symmetry of odd solutions to equations with fractional Laplacian
Sidy M. Djitte, Sven Jarohs
We present a symmetry result to solutions of equations involving the fractional Laplacian in a domain with at least two perpendicular symmetries. We show that if the solution is co…
Small order asymptotics of the Dirichlet eigenvalue problem for the fractional Laplacian
Pierre Aime Feulefack, Sven Jarohs, Tobias Weth
In this article, we study the asymptotics of Dirichlet eigenvalues and eigenfunctions of the fractional Laplacian in bounded open Lipschitz sets in the small order limit $…
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…
Foliated Schwarz symmetry of solutions to a cooperative system of equations involving nonlocal operators
Antonio Greco, Sven Jarohs
In this paper, we prove foliated Schwarz symmetry of solutions to a cooperatively coupled system of equations involving nonlocal operators. Here, the class of nonlocal operators co…