Partial regularity in nonlocal systems I
Analysis of PDEs
2025-01-16 v1
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.
Cite
@article{arxiv.2501.08405,
title = {Partial regularity in nonlocal systems I},
author = {Cristiana De Filippis and Giuseppe Mingione and Simon Nowak},
journal= {arXiv preprint arXiv:2501.08405},
year = {2025}
}
Comments
67 pages, comments are welcome!