Can I read Besov regularity for the Dirichlet integral fractional Laplacian in Lipschitz domains on EtoBox?

Besov regularity for the Dirichlet integral fractional Laplacian in Lipschitz domains by Borthagaray, Juan Pablo; Nochetto, Ricardo H. is a scholarly article available to read on EtoBox.

What is Besov regularity for the Dirichlet integral fractional Laplacian in Lipschitz domains about?

We prove Besov regularity estimates for the solution of the Dirichlet problem involving the integral fractional Laplacian of order $s$ in bounded Lipschitz domains $\Omega$: \[ \begin{aligned} \|u\|_{\dot{B}^{s+r}_{2,\infty}(\Omega)} \le C \|f\|_{L^2(\Omega)}, & \quad r = \min\{s,1/2\}, & \quad \mbox{if } s \neq 1/2, \\ \|u\|_{\dot{B}^{1-\epsilon}_{2,\infty}(\Omega)} \le C \|f\|_{L^2(\Omega)}, & \quad \epsilon \in (0,1), & \quad \mbox{if } s = 1/2, \end{aligned} \] with explicit dependence of $C$ on $s$ and $\epsilon$. 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.

Author

Borthagaray, Juan Pablo; Nochetto, Ricardo H.

Published

2021

Language

EN