Partial regularity in nonlocal systems I
Abstract
Solutions to nonlinear integro-differential systems are regular outside a negligible closed subset whose Hausdorff dimension can be explicitly bounded from above. This subset can be characterized using quantitative, universal energy thresholds for nonlocal excess functionals. The analysis is carried out via the use of nonlinear potentials and allows to derive fine properties of solutions under sharp assumptions on data and kernel coefficients.
Fields of Study & Subjects
Differential Equations and Boundary Problems
Stability and Controllability of Differential Equations
Spectral Theory in Mathematical Physics
Publication details
- Journal / source
- Advances in Mathematics
- Volume
- 502
- Pages
- 111152–111152
- Publication date
- 27 July 2026
- Language
- EN