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

Masoud Bayrami
, Morteza Fotouhi^*

^*Corresponding author for this work

Research output: Journal Publication › Article › peer-review

2 Citations (Scopus)

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

Free Keywords

35J92
35R35

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1007/s00526-024-02789-3

Cite this

@article{0db11074867841b593226f0d4820343d,

title = "Regularity in the two-phase Bernoulli problem for the p-Laplace operator",

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.",

keywords = "35J92, 35R35",

author = "Masoud Bayrami and Morteza Fotouhi",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.",

year = "2024",

month = sep,

doi = "10.1007/s00526-024-02789-3",

language = "English",

volume = "63",

journal = "Calculus of Variations and Partial Differential Equations",

issn = "0944-2669",

publisher = "Springer New York",

number = "7",

}

TY - JOUR

T1 - Regularity in the two-phase Bernoulli problem for the p-Laplace operator

AU - Bayrami, Masoud

AU - Fotouhi, Morteza

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.

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.

KW - 35J92

KW - 35R35

UR - https://www.scopus.com/pages/publications/85198618931

U2 - 10.1007/s00526-024-02789-3

DO - 10.1007/s00526-024-02789-3

M3 - Article

AN - SCOPUS:85198618931

SN - 0944-2669

VL - 63

JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

IS - 7

M1 - 183

ER -

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

Abstract

Free Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this