On a two-phase free boundary problem ruled by the infinity Laplacian

Damião J. Araújo; Eduardo V. Teixeira; José Miguel Urbano

doi:10.1007/s11856-021-2227-9

On a two-phase free boundary problem ruled by the infinity Laplacian

Damião J. Araújo, Eduardo V. Teixeira, José Miguel Urbano

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In this paper we consider a two-phase free boundary problem ruled by the infinity Laplacian. Our main result states that bounded viscosity solutions in B1 are universally Lipschitz continuous in B1/2, which is the optimal regularity for the problem. We make a new use of the Ishii–Lions’ method, which works as a surrogate for the lack of a monotonicity formula and is bound to be applicable in related problems.

Original language	English (US)
Pages (from-to)	773-785
Number of pages	13
Journal	Israel Journal of Mathematics
Volume	245
Issue number	2
DOIs	https://doi.org/10.1007/s11856-021-2227-9
State	Published - Oct 1 2021
Externally published	Yes

Bibliographical note

Generated from Scopus record by KAUST IRTS on 2023-02-15

Access to Document

10.1007/s11856-021-2227-9

Cite this

@article{28a252f24b6d4a1cb18008c2e9b9b96f,

title = "On a two-phase free boundary problem ruled by the infinity Laplacian",

abstract = "In this paper we consider a two-phase free boundary problem ruled by the infinity Laplacian. Our main result states that bounded viscosity solutions in B1 are universally Lipschitz continuous in B1/2, which is the optimal regularity for the problem. We make a new use of the Ishii–Lions{\textquoteright} method, which works as a surrogate for the lack of a monotonicity formula and is bound to be applicable in related problems.",

author = "Ara{\'u}jo, {Dami{\~a}o J.} and Teixeira, {Eduardo V.} and Urbano, {Jos{\'e} Miguel}",

note = "Generated from Scopus record by KAUST IRTS on 2023-02-15",

year = "2021",

month = oct,

day = "1",

doi = "10.1007/s11856-021-2227-9",

language = "English (US)",

volume = "245",

pages = "773--785",

journal = "Israel Journal of Mathematics",

issn = "0021-2172",

publisher = "Springer New York",

number = "2",

}

TY - JOUR

T1 - On a two-phase free boundary problem ruled by the infinity Laplacian

AU - Araújo, Damião J.

AU - Teixeira, Eduardo V.

AU - Urbano, José Miguel

N1 - Generated from Scopus record by KAUST IRTS on 2023-02-15

PY - 2021/10/1

Y1 - 2021/10/1

N2 - In this paper we consider a two-phase free boundary problem ruled by the infinity Laplacian. Our main result states that bounded viscosity solutions in B1 are universally Lipschitz continuous in B1/2, which is the optimal regularity for the problem. We make a new use of the Ishii–Lions’ method, which works as a surrogate for the lack of a monotonicity formula and is bound to be applicable in related problems.

AB - In this paper we consider a two-phase free boundary problem ruled by the infinity Laplacian. Our main result states that bounded viscosity solutions in B1 are universally Lipschitz continuous in B1/2, which is the optimal regularity for the problem. We make a new use of the Ishii–Lions’ method, which works as a surrogate for the lack of a monotonicity formula and is bound to be applicable in related problems.

UR - https://link.springer.com/10.1007/s11856-021-2227-9

UR - http://www.scopus.com/inward/record.url?scp=85118246275&partnerID=8YFLogxK

U2 - 10.1007/s11856-021-2227-9

DO - 10.1007/s11856-021-2227-9

M3 - Article

SN - 0021-2172

VL - 245

SP - 773

EP - 785

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 2

ER -

On a two-phase free boundary problem ruled by the infinity Laplacian

Abstract

Bibliographical note

Access to Document

Other files and links

Fingerprint

Cite this