A Two Phase Free Boundary Problem Related to Quadrature Domains

Behrouz Emamizadeh, Jyotshana V. Prajapat, Henrik Shahgholian

Research output: Journal PublicationArticlepeer-review

11 Citations (Scopus)


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 languageEnglish
Pages (from-to)119-138
Number of pages20
JournalPotential Analysis
Issue number2
Publication statusPublished - Feb 2011
Externally publishedYes


  • Free boundary
  • Quadrature domains
  • Two phase

ASJC Scopus subject areas

  • Analysis


Dive into the research topics of 'A Two Phase Free Boundary Problem Related to Quadrature Domains'. Together they form a unique fingerprint.

Cite this