WIAS Preprint No. 2154, (2015)

Interpolation inequalities in pattern formation


  • Cinti, Eleonora
  • Otto, Felix

2010 Mathematics Subject Classification

  • 49J40 47J20


  • Interpolation inequalities, optimal transport, pattern formation




We prove some interpolation inequalities which arise in the analysis of pattern formation in physics. They are the strong version of some already known estimates in weak form that are used to give a lower bound of the energy in many contexts (coarsening and branching in micromagnetics and superconductors). The main ingredient in the proof of our inequalities is a geometric construction which was first used by Choksi, Conti, Kohn, and one of the authors in citeCCKO in the study of branching in superconductors.

Appeared in

  • J. Funct. Anal., 271 (2016) pp. 1043--1376.

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