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

Masoud Bayrami; Morteza Fotouhi

doi:10.1007/s00526-024-02789-3

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

Research output: Journal Publication › Article › peer-review

Abstract

We show that any minimizer of the well-known ACF functional (for the p-Laplacian) constitutes a viscosity solution. This allows us to establish a uniform flatness decay at the two-phase free boundary points to improve the flatness, which 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. It is noteworthy that the analysis of branch points is also included.

Original language	English
Article number	183
Journal	Calculus of Variations and Partial Differential Equations
Volume	63
Issue number	7
DOIs	https://doi.org/10.1007/s00526-024-02789-3
Publication status	Published - Sept 2024
Externally published	Yes

Keywords

35J92
35R35

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1007/s00526-024-02789-3

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abstract = "We show that any minimizer of the well-known ACF functional (for the p-Laplacian) constitutes a viscosity solution. This allows us to establish a uniform flatness decay at the two-phase free boundary points to improve the flatness, which boils down to C1,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. It is noteworthy that the analysis of branch points is also included.",

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AU - Bayrami, Masoud

AU - Fotouhi, Morteza

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PY - 2024/9

Y1 - 2024/9

N2 - We show that any minimizer of the well-known ACF functional (for the p-Laplacian) constitutes a viscosity solution. This allows us to establish a uniform flatness decay at the two-phase free boundary points to improve the flatness, which boils down to C1,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. It is noteworthy that the analysis of branch points is also included.

AB - We show that any minimizer of the well-known ACF functional (for the p-Laplacian) constitutes a viscosity solution. This allows us to establish a uniform flatness decay at the two-phase free boundary points to improve the flatness, which boils down to C1,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. It is noteworthy that the analysis of branch points is also included.

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KW - 35R35

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M1 - 183

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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