Quasi-linear fractional-order operators in Lipschitz domains.
Resumen:
We prove Besov boundary regularity for solutions of the homogeneous Dirichlet problem for fractional-order quasi-linear operators with variable coefficients on Lipschitz domains Ω of Rd. Our estimates are consistent with the boundary behavior of solutions on smooth domains and apply to fractional p-Laplacians and operators with finite horizon. The proof exploits the underlying variational structure and uses a new and flexible local translation operator. We further apply these regularity estimates to derive novel error estimates for finite element approximations of fractional p-Laplacians and present several simulations that reveal the boundary behavior of solutions.
| 2024 | |
| Proyecto ANII - FCE_3_2022_1_172393 (Fondo Clemente Estable, modalidad II). | |
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Fractional quasi-linear operators Besov regularity Lipschitz domains Finite element approximation |
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| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/47504 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
