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.
All Science Journal Classification (ASJC) codes
- Control and Optimization
- Management Science and Operations Research
- Applied Mathematics