Lipschitz regularity of solutions to two-phase $p$-Laplacian free boundary problems with right hand side
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910054201950208 |
|---|---|
| author | Ferrari, Fausto Lederman, Claudia |
| author_facet | Ferrari, Fausto Lederman, Claudia |
| contents | We prove the local Lipschitz continuity of viscosity solutions for two-phase free boundary problems for the $p$-Laplacian with non-zero right hand side, where $p\in (1,\infty)$. This is the optimal regularity for the problem.
We also obtain the local Hölder continuity for a larger class of problems.
The results introduced here are new even in the homogeneous situation, that is, when the right hand side is zero.
Our work applies to merely viscosity solutions, which allows a wide applicability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_15024 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lipschitz regularity of solutions to two-phase $p$-Laplacian free boundary problems with right hand side Ferrari, Fausto Lederman, Claudia Analysis of PDEs 35R35, 35B65, 35J60, 35J70 We prove the local Lipschitz continuity of viscosity solutions for two-phase free boundary problems for the $p$-Laplacian with non-zero right hand side, where $p\in (1,\infty)$. This is the optimal regularity for the problem. We also obtain the local Hölder continuity for a larger class of problems. The results introduced here are new even in the homogeneous situation, that is, when the right hand side is zero. Our work applies to merely viscosity solutions, which allows a wide applicability. |
| title | Lipschitz regularity of solutions to two-phase $p$-Laplacian free boundary problems with right hand side |
| topic | Analysis of PDEs 35R35, 35B65, 35J60, 35J70 |
| url | https://arxiv.org/abs/2603.15024 |