Calculus of Variations and Geometric Measure Theory
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E. Cinti - F. Otto

Interpolation inequalities in pattern formation

created by cinti on 02 Sep 2015
modified on 27 Jul 2016

[BibTeX]

Accepted Paper

Inserted: 2 sep 2015
Last Updated: 27 jul 2016

Journal: J. Funct. Anal.
Year: 2016

Abstract:

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.


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