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 geometric 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.
Area Quasi-minimizing Partitions with a Graphical Constraint: Relaxation and Two-Dimensional Partial Regularity / Bonacini, M.; Cristoferi, R.. - In: JOURNAL OF NONLINEAR SCIENCE. - ISSN 0938-8974. - 32:6(2022), pp. 9301-9353. [10.1007/s00332-022-09852-3]
Area Quasi-minimizing Partitions with a Graphical Constraint: Relaxation and Two-Dimensional Partial Regularity
Bonacini M.;Cristoferi R.
2022-01-01
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 geometric 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.File | Dimensione | Formato | |
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Bonacini - Cristoferi, Area quasi-minimizing partitions with a graphical constraint.pdf
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