dc.contributor.author |
Ros-Oton, X. |
dc.contributor.author |
Torres-Latorre, C. |
dc.date.accessioned |
2024-03-04T11:25:43Z |
dc.date.available |
2024-03-04T11:25:43Z |
dc.date.issued |
2023-09-29 |
dc.identifier.uri |
http://hdl.handle.net/2072/537457 |
dc.description.sponsorship |
Both authors were supported by the European Research Council (ERC) under the Grant Agreement No 801867, and the AEI project PID2021‐125021NAI00 (Spain). X.R. was supported by AGAUR Grant 2021 SGR 00087 (Catalunya), by AEI Grant RED2022‐134784‐T funded by MCIN/AEI/10.13039/501100011033 (Spain), and by the AEI through the María de Maeztu Program for Centres and Units of Excellence in R&D (CEX2020‐001084‐M). |
dc.format.extent |
42 p. |
dc.language.iso |
eng |
dc.publisher |
John Wiley and Sons Inc |
dc.relation.ispartof |
Communications on Pure and Applied Mathematics |
dc.rights |
L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: http://creativecommons.org/licenses/by-nc-nd/4.0/ |
dc.source |
RECERCAT (Dipòsit de la Recerca de Catalunya) |
dc.subject.other |
parabolic operators, supercritical regime, elliptic setting |
dc.title |
Optimal regularity for supercritical parabolic obstacle problems |
dc.type |
info:eu-repo/semantics/article |
dc.type |
info:eu-repo/semantics/publishedVersion |
dc.embargo.terms |
cap |
dc.identifier.doi |
10.1002/cpa.22166 |
dc.rights.accessLevel |
info:eu-repo/semantics/openAccess |
dc.description.abstract |
We study the obstacle problem for parabolic operators of the type (Formula presented.), where L is an elliptic integro-differential operator of order 2s, such as (Formula presented.), in the supercritical regime (Formula presented.). The best result in this context was due to Caffarelli and Figalli, who established the (Formula presented.) regularity of solutions for the case (Formula presented.), the same regularity as in the elliptic setting. Here we prove for the first time that solutions are actually more regular than in the elliptic case. More precisely, we show that they are C1, 1 in space and time, and that this is optimal. We also deduce the (Formula presented.) regularity of the free boundary. Moreover, at all free boundary points (Formula presented.), we establish the following expansion: (Formula presented.) with (Formula presented.), (Formula presented.) and (Formula presented.). © 2023 The Authors. Communications on Pure and Applied Mathematics published by Courant Institute of Mathematics and Wiley Periodicals LLC. |