Addendum: Local elliptic regularity for the Dirichlet fractional Laplacian
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Fecha
2017
Autores
Biccari, Umberto
Warma, Mahamadi
Zuazua, Enrique
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Editor
Walter de Gruyter GmbH
Resumen
In [1], for 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 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.
Palabras clave
Fractional Laplacian
Dirichlet boundary condition
Weak solutions
Local regularity
Dirichlet boundary condition
Weak solutions
Local regularity
Descripción
Materias
Cita
Biccari, 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-2017-6020