Convergence rates of the fractional to the local Dirichlet problem
Abstract
We prove non-asymptotic rates of convergence in the $W^{s,2}(\mathbb R^d)$-norm for the solution of the fractional Dirichlet problem to the solution of the local Dirichlet problem as $s\uparrow 1$. For regular enough boundary values we get a rate of order $\sqrt{1-s}$, while for less regular data the rate is of order $\sqrt{(1-s)|\log(1-s)|}$. We also obtain results when the right hand side depends on $s$, and our error estimates are true for all $s\in(0,1)$. The proofs use variational arguments to deduce rates in the fractional Sobolev norm from energy estimates between the fractional and the standard Dirichlet energy.
Fields of Study & Subjects
Fractional Differential Equations Solutions
Nonlinear Differential Equations Analysis
Differential Equations and Boundary Problems
Publication details
- Journal / source
- Journal of Differential Equations
- Publisher
- Elsevier BV
- Volume
- 463
- Pages
- 114173–114173
- Publication date
- 6 February 2026
- Language
- EN