Duality theorem for a three-phase partition problem

H. Kawasaki

    Research output: Contribution to journalArticlepeer-review

    1 Citation (Scopus)

    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⊂ 2 into three subdomains having least interfacial area. Ikota and Yanagida investigated stability and instability for stationary curves with one triple junction and for stationary binary-tree 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 three-phase partition problem, and present a duality theorem.

    Original languageEnglish
    Pages (from-to)1-10
    Number of pages10
    JournalJournal of Optimization Theory and Applications
    Volume137
    Issue number1
    DOIs
    Publication statusPublished - Apr 2008

    All Science Journal Classification (ASJC) codes

    • Control and Optimization
    • Applied Mathematics
    • Management Science and Operations Research

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