Regularity in the two-phase Bernoulli problem for the $p$-Laplace operator
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866912454691258368 |
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| author | Bayrami-Aminlouee, Masoud Fotouhi, Morteza |
| author_facet | Bayrami-Aminlouee, Masoud Fotouhi, Morteza |
| contents | We show that any minimizer of the well-known ACF functional (for the $p$-Laplacian) is a viscosity solution. This allows us to establish a uniform flatness decay at the two-phase free boundary points to improve the flatness, that boils down to $C^{1,η}$ regularity of the flat part of the free boundary. This result, in turn, is used to prove the Lipschitz regularity of minimizers by a dichotomy argument. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_11775 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Regularity in the two-phase Bernoulli problem for the $p$-Laplace operator Bayrami-Aminlouee, Masoud Fotouhi, Morteza Analysis of PDEs 35R35, 35J92 We show that any minimizer of the well-known ACF functional (for the $p$-Laplacian) is a viscosity solution. This allows us to establish a uniform flatness decay at the two-phase free boundary points to improve the flatness, that boils down to $C^{1,η}$ regularity of the flat part of the free boundary. This result, in turn, is used to prove the Lipschitz regularity of minimizers by a dichotomy argument. |
| title | Regularity in the two-phase Bernoulli problem for the $p$-Laplace operator |
| topic | Analysis of PDEs 35R35, 35J92 |
| url | https://arxiv.org/abs/2301.11775 |