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arXiv · 2107.13325

Area quasi-minimizing partitions with a graphical constraint: relaxation and two-dimensional partial regularity

Marco Bonacini·Riccardo Cristoferi
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Abstract

We consider a variational model for periodic partitions of the upper half-space into three regions, where two of them have prescribed volume and are subject to the geometrical constraint that their union is the subgraph of a function, whose graph is a free surface. The energy of a configuration is given by the weighted sum of the areas of the interfaces between the different regions, and a general volume-order term. We establish existence of minimizing configurations via relaxation of the energy involved, in any dimension. Moreover, we prove partial regularity results for volume-constrained minimizers in two space dimensions. Thin films of diblock copolymers are a possible application and motivation for considering this problem.

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Marco Bonacini, Riccardo Cristoferi. 2021-07-28. Area quasi-minimizing partitions with a graphical constraint: relaxation and two-dimensional partial regularity. https://doi.org/10.1007/s00332-022-09852-3

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