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arXiv · 2301.11775

Regularity in the two-phase Bernoulli problem for the $p$-Laplace operator

Masoud Bayrami-Aminlouee·Morteza Fotouhi
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Abstract

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 $C^{1,\eta}$ 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.

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Masoud Bayrami-Aminlouee, Morteza Fotouhi. 2023-01-11. Regularity in the two-phase Bernoulli problem for the $p$-Laplace operator. https://doi.org/10.1007/s00526-024-02789-3

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