Duality theorem for a three-phase partition problem

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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⊂ 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
  • Management Science and Operations Research
  • Applied Mathematics

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