Search

MiS Preprint Repository

Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.

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:
Sep 4, 2015
Published:
Sep 4, 2015
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