A Two Phase Free Boundary Problem Related to Quadrature Domains

Behrouz Emamizadeh; Jyotshana V. Prajapat; Henrik Shahgholian

doi:10.1007/s11118-010-9184-y

A Two Phase Free Boundary Problem Related to Quadrature Domains

Behrouz Emamizadeh, Jyotshana V. Prajapat, Henrik Shahgholian

Research output: Journal Publication › Article › peer-review

11 Citations (Scopus)

Abstract

In this paper we introduce a two phase version of the well-known Quadrature Domain theory, which is a generalized (sub)mean value property for (sub)harmonic functions. In concrete terms, and after reformulation into its PDE version the problem boils down to finding solution to, where λ± >0 are given constants and μ^±, are non-negative bounded Radon measures, with compact support. Our primary concern is to discuss existence and geometric properties of solutions.

Original language	English
Pages (from-to)	119-138
Number of pages	20
Journal	Potential Analysis
Volume	34
Issue number	2
DOIs	https://doi.org/10.1007/s11118-010-9184-y
Publication status	Published - Feb 2011
Externally published	Yes

Keywords

Free boundary
Quadrature domains
Two phase

ASJC Scopus subject areas

Analysis

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10.1007/s11118-010-9184-y

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title = "A Two Phase Free Boundary Problem Related to Quadrature Domains",

abstract = "In this paper we introduce a two phase version of the well-known Quadrature Domain theory, which is a generalized (sub)mean value property for (sub)harmonic functions. In concrete terms, and after reformulation into its PDE version the problem boils down to finding solution to, where λ± >0 are given constants and μ±, are non-negative bounded Radon measures, with compact support. Our primary concern is to discuss existence and geometric properties of solutions.",

keywords = "Free boundary, Quadrature domains, Two phase",

author = "Behrouz Emamizadeh and Prajapat, {Jyotshana V.} and Henrik Shahgholian",

note = "Funding Information: H. Shahgholian was supported in part by Swedish Research Council. This work was started when H. Shahgholian was visiting The Petroleum Institute. The authors are grateful to the referee for valuable suggestions and comments.",

year = "2011",

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doi = "10.1007/s11118-010-9184-y",

language = "English",

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AU - Emamizadeh, Behrouz

AU - Prajapat, Jyotshana V.

AU - Shahgholian, Henrik

N1 - Funding Information: H. Shahgholian was supported in part by Swedish Research Council. This work was started when H. Shahgholian was visiting The Petroleum Institute. The authors are grateful to the referee for valuable suggestions and comments.

PY - 2011/2

Y1 - 2011/2

N2 - In this paper we introduce a two phase version of the well-known Quadrature Domain theory, which is a generalized (sub)mean value property for (sub)harmonic functions. In concrete terms, and after reformulation into its PDE version the problem boils down to finding solution to, where λ± >0 are given constants and μ±, are non-negative bounded Radon measures, with compact support. Our primary concern is to discuss existence and geometric properties of solutions.

AB - In this paper we introduce a two phase version of the well-known Quadrature Domain theory, which is a generalized (sub)mean value property for (sub)harmonic functions. In concrete terms, and after reformulation into its PDE version the problem boils down to finding solution to, where λ± >0 are given constants and μ±, are non-negative bounded Radon measures, with compact support. Our primary concern is to discuss existence and geometric properties of solutions.

KW - Free boundary

KW - Quadrature domains

KW - Two phase

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DO - 10.1007/s11118-010-9184-y

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SP - 119

EP - 138

JO - Potential Analysis

JF - Potential Analysis

IS - 2

ER -

A Two Phase Free Boundary Problem Related to Quadrature Domains

Abstract

Keywords

ASJC Scopus subject areas

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