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In some nonlinear diffusive phenomena, the systems have three or more stable states. Sternberg and Zeimer (Ref. 1) established the existence of local minimizers to the problem of partitioning certain ...domain $ Omega subset R^2 $ into three subdomains having least interfacial area. Ikota and Yanagida investigated stability and instability for stationary curves with one triple junction in (Ref. 2) and for stationary binary tree type interfaces in (Ref. 3). In this paper, we consider a static version of the partitioning problem with a triple junction and present a duality theorem. The novelity of our duality theorem is tha it is based on separation of three convex sets by a triangle.続きを見る
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