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MiS Preprint

Interpolation inequalities in pattern formation

Eleonora Cinti and Felix Otto


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.

Sep 4, 2015
Sep 4, 2015
MSC Codes:
49J40, 47J20
Interpolation inequalities, optimal transport, pattern formation

Related publications

2016 Repository Open Access
Eleonora Cinti and Felix Otto

Interpolation inequalities in pattern formation

In: Journal of functional analysis, 271 (2016) 11, pp. 3348-3392