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

• Katarina Bellova ^[1] ; Antoine Julia ^[2] ; Felix Otto ^[3]
  1. [1] University of Duisburg-Essen

     University of Duisburg-Essen

     Kreisfreie Stadt Essen, Alemania

     
  2. [2] University of Paris-Saclay

     University of Paris-Saclay

     Arrondissement de Palaiseau, Francia

     
  3. [3] Max Planck Institute for Mathematics in the Sciences

     Max Planck Institute for Mathematics in the Sciences

     Kreisfreie Stadt Leipzig, Alemania

     

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• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 38, Nº 3, 2022, págs. 783-822
• Idioma: inglés
• DOI: 10.4171/RMI/1308
• Texto completo no disponible (Saber más ...)
• Resumen

  • We consider a variational model for a charge density u∈{−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.