arXiv Analytics

Sign in

arXiv:2106.00439 [math.AP]AbstractReferencesReviewsResources

Regularity of flat free boundaries for a $p(x)$-Laplacian problem with right hand side

Fausto Ferrari, Claudia Lederman

Published 2021-06-01Version 1

We consider viscosity solutions to a one-phase free boundary problem for the $p(x)$-Laplacian with non-zero right hand side. We apply the tools developed in \cite{D} to prove that flat free boundaries are $C^{1,\alpha}$. Moreover, we obtain some new results for the operator under consideration that are of independent interest.

Comments: arXiv admin note: text overlap with arXiv:0912.2057 by other authors
Categories: math.AP
Subjects: 35R35, 35R35, 35B65, 35J60, 35J70
Related articles: Most relevant | Search more
arXiv:2305.07418 [math.AP] (Published 2023-05-12)
Regularity of Lipschitz free boundaries for a $p(x)$-Laplacian problem with right hand side
arXiv:0912.2057 [math.AP] (Published 2009-12-10)
Free boundary regularity for a problem with right hand side
arXiv:1412.4106 [math.AP] (Published 2014-12-12)
Structure of one-phase free boundaries in the plane

Links

Toolbox