Abstract
AbstractIn this work we study nonlocal operators and corresponding spaces with a focus on operators of order near zero. We investigate the interior regularity of eigenfunctions and of weak solutions to the associated Poisson problem depending on the regularity of the right-hand side. Our method exploits the variational structure of the problem and we prove that eigenfunctions are of class $$C^{\infty }$$
C
∞
if the kernel satisfies this property away from its singularity. Similarly in this case, if in the Poisson problem the right-hand is of class $$C^{\infty }$$
C
∞
, then also any weak solution is of class $$C^{\infty }$$
C
∞
.
Funder
Johann Wolfgang Goethe-Universität, Frankfurt am Main
Publisher
Springer Science and Business Media LLC
Cited by
4 articles.
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