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Title of Journal: J Optim Theory Appl

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Abbravation: Journal of Optimization Theory and Applications

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Springer US

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1573-2878

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Duality Theorem for a ThreePhase Partition Proble

Authors: H Kawasaki
Publish Date: 2008/01/26
Volume: 137, Issue: 1, Pages: 1-10
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Abstract

In some nonlinear diffusive phenomena the systems have three or more stable states Sternberg and Zeimer established the existence of minimal solutions for the problem of partitioning a certain domain Ω⊂ℝ2 into three subdomains having least interfacial area Ikota and Yanagida investigated stability and instability for stationary curves with one triple junction and for stationary binarytree type interfaces In this paper we introduce a new concept of separation of three convex sets by a triangle define a dual problem to the threephase partition problem and present a duality theoremThis research was partially supported by Kyushu University 21st Century COE Program Development of Dynamic Mathematics with High Functionality and by the GrantinAid for General Scientific Research from the Japan Society for the Promotion of Science 14340037

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