A free boundary problem for an elliptic system

Morteza Fotouhi; Henrik Shahgholian; Georg S. Weiss

doi:10.1016/j.jde.2021.02.050

A free boundary problem for an elliptic system

Morteza Fotouhi, Henrik Shahgholian, Georg S. Weiss

Research output: Journal Publication › Article › peer-review

8 Citations (Scopus)

Abstract

We study solutions and the free boundary ∂{|u|>0} of the sublinear system Δu=λ₊(x)|u⁺|^q−1u⁺−λ₋(x)|u⁻|^q−1u⁻, from a regularity point of view. For λ_±(x)>0 and Hölder, and 0<q<1, we apply the epiperimetric inequality approach and show C^1,β-regularity for the free boundary at asymptotically flat points.

Original language	English
Pages (from-to)	126-155
Number of pages	30
Journal	Journal of Differential Equations
Volume	284
DOIs	https://doi.org/10.1016/j.jde.2021.02.050
Publication status	Published - 25 May 2021
Externally published	Yes

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jde.2021.02.050

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title = "A free boundary problem for an elliptic system",

abstract = "We study solutions and the free boundary ∂\{|u|>0\} of the sublinear system Δu=λ+(x)|u+|q−1u+−λ−(x)|u−|q−1u−, from a regularity point of view. For λ±(x)>0 and H{\"o}lder, and 01,β-regularity for the free boundary at asymptotically flat points.",

author = "Morteza Fotouhi and Henrik Shahgholian and Weiss, \{Georg S.\}",

note = "Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",

year = "2021",

month = may,

day = "25",

doi = "10.1016/j.jde.2021.02.050",

language = "English",

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journal = "Journal of Differential Equations",

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T1 - A free boundary problem for an elliptic system

AU - Fotouhi, Morteza

AU - Shahgholian, Henrik

AU - Weiss, Georg S.

PY - 2021/5/25

Y1 - 2021/5/25

N2 - We study solutions and the free boundary ∂{|u|>0} of the sublinear system Δu=λ+(x)|u+|q−1u+−λ−(x)|u−|q−1u−, from a regularity point of view. For λ±(x)>0 and Hölder, and 01,β-regularity for the free boundary at asymptotically flat points.

AB - We study solutions and the free boundary ∂{|u|>0} of the sublinear system Δu=λ+(x)|u+|q−1u+−λ−(x)|u−|q−1u−, from a regularity point of view. For λ±(x)>0 and Hölder, and 01,β-regularity for the free boundary at asymptotically flat points.

UR - https://www.scopus.com/pages/publications/85101905642

U2 - 10.1016/j.jde.2021.02.050

DO - 10.1016/j.jde.2021.02.050

M3 - Article

AN - SCOPUS:85101905642

SN - 0022-0396

VL - 284

SP - 126

EP - 155

JO - Journal of Differential Equations

JF - Journal of Differential Equations

ER -

A free boundary problem for an elliptic system

Abstract

ASJC Scopus subject areas

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