Regularity for nonlocal equations with local Neumann boundary conditions
Abstract
In this article we establish fine results on the boundary behavior of solutions to nonlocal equations in $C^{k,γ}$ domains which satisfy local Neumann conditions on the boundary. Such solutions typically blow up at the boundary like $v \asymp d^{s-1}$ and are sometimes called large solutions. In this setup we prove optimal regularity results for the quotients $v/d^{s-1}$, depending on the regularity of the domain and on the data of the problem. The results of this article will be important in a forthcoming work on nonlocal free boundary problems.
Fields of Study & Subjects
Differential Equations and Boundary Problems
Advanced Mathematical Modeling in Engineering
Numerical methods in inverse problems
Publication details
- Journal / source
- Analysis & PDE
- Volume
- 19
- Issue
- 2
- Pages
- 353–411
- Publication date
- 22 January 2026
- Language
- EN