Free boundary regularity for a one-phase problem with non-standard growth

FERRARI, FAUSTO; LEDERMAN, CLAUDIA

Matemática Aplicada, Computacional e Industrial (MACI) - ISSN 2314-2382

Asociación Argentina de Matemática Aplicada, Computacional e Industrial

Lugar: Santa Fe; Año: 2023 vol. 2023 p. 211 - 214

2314-3282

We present results in cite{FL1, FL2} for viscosity solutions to a one-phase free boundary problem for the $p(x)$-Laplacian with non-zero right hand side. We prove that viscosity solutions are locally Lipschitz continuous, which is the optimal regularity. Then we prove that flat and Lipschitz free boundaries of viscosity solutions are $C^{1,alpha}$. We also introduce some applications and moreover, we obtain new results for the operator considered.