Continuity of solutions to equations with weakly singular nonlocal operators
Abstract
We prove boundedness and regularity estimates for weak solutions to a class of linear nonlocal equations involving integro-differential operators with almost no order of differentiability. In particular, we show that bounded weak solutions are continuous, and we provide a uniform a-priori estimate for the modulus of continuity. In contrast to earlier works, we allow the nonlocal operators to be highly anisotropic and weakly singular, and we allow the associated kernel functions to vanish close to the singularity.
Fields of Study & Subjects
Differential Equations and Boundary Problems
Advanced Mathematical Modeling in Engineering
Numerical methods in inverse problems
Publication details
- Journal / source
- Transactions of the American Mathematical Society
- Volume
- 379
- Issue
- 10
- Pages
- 7097–7128
- Publication date
- 27 May 2026
- Language
- EN