Biccari, UmbertoWarma, MahamadiZuazua, Enrique2025-01-072025-01-072017Biccari, U., Warma, M., & Zuazua, E. (2017). Addendum: Local Elliptic Regularity for the Dirichlet Fractional Laplacian. Advanced Nonlinear Studies, 17(4), 837-839. https://doi.org/10.1515/ANS-2017-60201536-136510.1515/ANS-2017-6020http://hdl.handle.net/20.500.14454/2196In [1], for 1 < p < 1<p< ∞, we proved the W loc 2 s p W 2s,p loc local elliptic regularity of weak solutions to the Dirichlet problem associated with the fractional Laplacian (- Δ) s -Δ s on an arbitrary bounded open set of N R N. Here we make a more precise and rigorous statement. In fact, for 1 < p < 2 1<p<2 and s 1 2 s 1 2, local regularity does not hold in the Sobolev space W loc 2 s p W 2s,p loc, but rather in the larger Besov space (B p 2 2 s) loc (B 2s p,2 loc.engFractional LaplacianDirichlet boundary conditionWeak solutionsLocal regularityjournal article2025-01-07