Besov regularity for the Dirichlet integral fractional Laplacian in Lipschitz domains.
Resumen:
We prove Besov regularity estimates for the solution of the Dirichlet problem involving the integral fractional Laplacian of order s in bounded Lipschitz domains Ω: ∥u∥B˙s+r2,∞(Ω)≤C∥f∥L2(Ω),∥u∥B˙1−ϵ2,∞(Ω)≤C∥f∥L2(Ω),r=min{s,1/2},ϵ∈(0,1),if s≠1/2,if s=1/2, with explicit dependence of C on s and ϵ. These estimates are consistent with the regularity on smooth domains and show that there is no loss of regularity due to Lipschitz boundaries. The proof uses elementary ingredients, such as the variational structure of the problem and the difference quotient technique.
| 2022 | |
| Juan Pablo Borthagaray ha sido financiado en parte por beca DMS-1411808 de la NSF y beca 2019-068 del Fondo Vaz Ferreira. | |
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Fractional Laplacian Lipschitz domains Regularity estimates |
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| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/47834 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
