Partitions with Prescribed Mean Curvatures
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چکیده
We consider a certain variational problem on Caccioppoli partitions with countably many components, which models immiscible fluids as well as variational image segmentation, and generalizes the well-known problem with prescribed mean curvature. We prove existence and regularity results, and finally show some explicit examples of minimizers. Introduction In this paper we consider a variational problem on Caccioppoli partitions, i.e. partitions whose interface area is locally finite. More precisely, we will be concerned with the following problem: given Ω ⊂ R open, minimize ΦH(U; Ω) := P (U,Ω) + inf (Ui)i ∑
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تاریخ انتشار 2008