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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
56/2015

Interpolation inequalities in pattern formation

Eleonora Cinti and Felix Otto

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.

Received:
04.09.15
Published:
04.09.15
MSC Codes:
49J40, 47J20
Keywords:
Interpolation inequalities, optimal transport, pattern formation

Related publications

inJournal
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