Addendum: Local elliptic regularity for the Dirichlet fractional Laplacian


Biccari U., Warma M., Zuazua E. Addendum: Local elliptic regularity for the Dirichlet fractional Laplacian
Advanced Nonlinear Studies 17 (2017), 837-839. DOI: 10.1515/ans-2017-6020

Abstract:
In [1], for 1<p<\infty, we proved the W_{\textrm{loc}}^{2s,p} local elliptic regularity of weak solutions to the Dirichlet problem associated with the fractional Laplacian (-\Delta)^s on an arbitrary bounded open set of \mathbb{R}^N. Here we make a more precise and rigorous statement. In fact, for 1<p<2 and s\neq\frac{1}{2}, local regularity does not hold in the Sobolev space W_{\textrm{loc}}^{2s,p}, but rather in the larger Besov space (B^{2s}_{p,2})_{\textrm{loc}}.

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