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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, p. 119-138Article 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, p. 119-138
Keyword [en]
Free boundary, Two phase, Quadrature domains
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-30506DOI: 10.1007/s11118-010-9184-yISI: 000286102600002Scopus ID: 2-s2.0-79751529344OAI: oai:DiVA.org:kth-30506DiVA, id: diva2:404532
Funder
Swedish Research Council
Note
QC 20110317Available from: 2011-03-17 Created: 2011-02-28 Last updated: 2017-12-11Bibliographically approved

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Shahgholian, Henrik

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