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Two-and multi-phase quadrature surfaces
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2017 (English)In: Communications on Pure and Applied Analysis, ISSN 1534-0392, E-ISSN 1553-5258, Vol. 16, no 6, p. 2023-2045Article in journal (Refereed) Published
Abstract [en]

In this paper we shall initiate the study of the two-and multi-phase quadrature surfaces (QS), which amounts to a two/multi-phase free boundary problems of Bernoulli type. The problem is studied mostly from a potential theoretic point of view that (for two-phase case) relates to integral representation where dsx is the surface measure, μ = μ+-μ-is given measure with support in (a priori unknown domain) ω = ω+ [ω-, g is a given smooth positive function, and the integral holds for all functions h, which are harmonic on ω. Our approach is based on minimization of the corresponding two-and multiphase functional and the use of its one-phase version as a barrier. We prove several results concerning existence, qualitative behavior, and regularity theory for solutions. A central result in our study states that three or more junction points do not appear.

Place, publisher, year, edition, pages
American Institute of Mathematical Sciences, 2017. Vol. 16, no 6, p. 2023-2045
Keywords [en]
Bernoulli boundary condition, Free boundary, Two-phase quadrature surface
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-212207DOI: 10.3934/cpaa.2017099ISI: 000411803300005Scopus ID: 2-s2.0-85026468917OAI: oai:DiVA.org:kth-212207DiVA, id: diva2:1134573
Note

QC 20170821

Available from: 2017-08-21 Created: 2017-08-21 Last updated: 2017-10-16Bibliographically approved

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