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A Two Phase Free Boundary Problem Related to Quadrature Domains
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-1316-7913
2011 (English)In: Potential Analysis, ISSN 0926-2601, E-ISSN 1572-929X, Vol. 34, no 2, 119-138 p.Article in journal (Refereed) Published
Abstract [en]

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 -Delta u=(mu(+)-lambda(+))(chi{u>0}) - (mu(-) - lambda(-))(chi{u<0}) in IRN. where lambda(+/-) >0 are given constants and mu(+/-), are non-negative bounded Radon measures, with compact support. Our primary concern is to discuss existence and geometric properties of solutions.

Place, publisher, year, edition, pages
2011. Vol. 34, no 2, 119-138 p.
Keyword [en]
Free boundary, Two phase, Quadrature domains
National Category
URN: urn:nbn:se:kth:diva-30506DOI: 10.1007/s11118-010-9184-yISI: 000286102600002ScopusID: 2-s2.0-79751529344OAI: diva2:404532
Swedish Research Council
QC 20110317Available from: 2011-03-17 Created: 2011-02-28 Last updated: 2012-04-14Bibliographically approved

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Shahgholian, Henrik
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