Quasi-linear fractional-order operators in Lipschitz domains

Autor:	Borthagaray, Juan Pablo, Li, Wenbo, Nochetto, Ricardo H.
Rok vydání:	2023
Předmět:	Mathematics - Analysis of PDEs Mathematics - Numerical Analysis
Druh dokumentu:	Working Paper
Popis:	We prove Besov boundary regularity for solutions of the homogeneous Dirichlet problem for fractional-order quasi-linear operators with variable coefficients on Lipschitz domains $\Omega$ of $\mathbb{R}^d$. 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.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2305.17818 Zobrazit plný text záznamu View this record from Arxiv