# Addendum: Local elliptic regularity for the Dirichlet fractional Laplacian

U. Biccari, M. Warma, E. Zuazua Addendum: Local elliptic regularity for the Dirichlet fractional Laplacian
Adv. Nonlinear Stud., Vol. 17, Nr. 4 (2017), pp. 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}}