TY - JOUR
T1 - Duality theorem for a three-phase partition problem
AU - Kawasaki, H.
N1 - Funding Information:
The author thanks Professor F. Giannessi for valuable comments, especially on Gale and Klee-type separation theorems. This research was partially supported by Kyushu University 21st Century COE Program (Development of Dynamic Mathematics with High Functionality) and by the Grant-in-Aid for General Scientific Research from the Japan Society for the Promotion of Science 14340037.
PY - 2008/4
Y1 - 2008/4
N2 - 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.
AB - 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.
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U2 - 10.1007/s10957-007-9266-1
DO - 10.1007/s10957-007-9266-1
M3 - Article
AN - SCOPUS:38349107630
SN - 0022-3239
VL - 137
SP - 1
EP - 10
JO - Journal of Optimization Theory and Applications
JF - Journal of Optimization Theory and Applications
IS - 1
ER -