Duality Theorem for a Three-Phase Partition Problem

H. Kawasaki ()
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H. Kawasaki: Kyushu University

Journal of Optimization Theory and Applications, 2008, vol. 137, issue 1, No 1, 10 pages

Abstract: 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 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.

Keywords: Duality theorems; Separation theorems; Convex sets; Partition problems; Triangles (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/s10957-007-9266-1

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