ThefailureofDeGiorgi–Nashtheoryinthevectorialsettingopens the way to the study of partial regularity, namely smoothness of solutions outside a negligible singular set. This is a classical topic in regularity theory. We give an account of some classical local partial regularity results, and of more recent developments in the nonlocal setting, drawing a parallel between the two. Emphasis is put on the structure and size of the singular set of solutions.
NONLOCAL PARTIAL REGULARITY / De Filippis, C., Mingione, G., Nowak, S.. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - 57:0(2026), pp. 443-495. [10.3934/dcds.2026133]
NONLOCAL PARTIAL REGULARITY
De Filippis C.
;Mingione G.;
2026-01-01
Abstract
ThefailureofDeGiorgi–Nashtheoryinthevectorialsettingopens the way to the study of partial regularity, namely smoothness of solutions outside a negligible singular set. This is a classical topic in regularity theory. We give an account of some classical local partial regularity results, and of more recent developments in the nonlocal setting, drawing a parallel between the two. Emphasis is put on the structure and size of the singular set of solutions.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
