Calculus of Variations and Geometric Measure Theory
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M. Bonacini - R. Cristoferi

Thin films of diblock copolymers: existence and two-dimensional regularity of minimizing configurations

created by cristoferi on 14 Sep 2021

[BibTeX]

Submitted Paper

Inserted: 14 sep 2021
Last Updated: 14 sep 2021

Year: 2021

ArXiv: 2107.13325 PDF

Abstract:

We introduce a variational model for the study of thin films of diblock copolymers. We establish existence of minimizing configurations via relaxation of the energy involved. Moreover, we prove partial regularity results for mass-constrained minimizers in two space dimensions. To show this last result, we develop a two-dimensional regularity theory for partitions with quasi-minimal surface area, subject to an additional graph constraint.

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