Interpolation inequalities in pattern formation
Eleonora Cinti and Felix Otto
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Submission date: 04. Sep. 2015
published in: Journal of functional analysis, 271 (2016) 11, p. 3348-3392
DOI number (of the published article): 10.1016/j.jfa.2016.05.007
MSC-Numbers: 49J40, 47J20
Keywords and phrases: Interpolation inequalities, optimal transport, pattern formation
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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 the study of branching in superconductors.