JournalsrmiVol. 38, No. 3pp. 783–822

Uniform energy distribution in a pattern-forming system of surface charges

  • Katarina Bellova

    University of Duisburg-Essen, Germany
  • Antoine Julia

    Université Paris-Saclay, Orsay, France
  • Felix Otto

    Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany
Uniform energy distribution in a pattern-forming system of surface charges cover
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Abstract

We consider a variational model for a charge density u{1,1}u\in\{-1,1\} on a (hyper)plane, with a short-range attraction coming from the interfacial energy and a long-range repulsion coming from the electrostatic energy. This competition leads to pattern formation. We prove that the interfacial energy density is (asymptotically) equidistributed at scales large compared to the scale of the pattern. We follow the strategy laid out by Alberti, Choksi and Otto (2009). The challenge comes from the reduced screening capabilities of surface charges compared to the volume charges considered in the aforementioned work.

Cite this article

Katarina Bellova, Antoine Julia, Felix Otto, Uniform energy distribution in a pattern-forming system of surface charges. Rev. Mat. Iberoam. 38 (2022), no. 3, pp. 783–822

DOI 10.4171/RMI/1308