Solutions to nonlinear vectorial integro-differential equations 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.
Partial regularity in nonlocal systems I / De Filippis, C., Mingione, G., Nowak, S.. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - 502:(2026). [10.1016/j.aim.2026.111152]
Partial regularity in nonlocal systems I
De Filippis C.;Mingione G.
;
2026-01-01
Abstract
Solutions to nonlinear vectorial integro-differential equations 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.File in questo prodotto:
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