Abstract
AbstractWe prove Sobolev regularity for distributional solutions to the Dirichlet problem for generators of 2s-stable processes and exterior data, inhomogeneity in weighted $$L^2$$
L
2
-spaces. This class of operators includes the fractional Laplacian. For these rough exterior data the theory of weak variational solutions is not applicable. Our regularity estimate is robust in the limit $$s\rightarrow 1-$$
s
→
1
-
which allows us to recover the local theory.
Funder
Deutsche Forschungsgemeinschaft
Universität Bielefeld
Publisher
Springer Science and Business Media LLC
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