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Communications in Mathematical Physics

, Volume 322, Issue 2, pp 515–557 | Cite as

Minimality via Second Variation for a Nonlocal Isoperimetric Problem

  • E. Acerbi
  • N. FuscoEmail author
  • M. Morini
Article

Abstract

We discuss the local minimality of certain configurations for a nonlocal isoperimetric problem used to model microphase separation in diblock copolymer melts. We show that critical configurations with positive second variation are local minimizers of the nonlocal area functional and, in fact, satisfy a quantitative isoperimetric inequality with respect to sets that are L 1-close. The link with local minimizers for the diffuse-interface Ohta-Kawasaki energy is also discussed. As a byproduct of the quantitative estimate, we get new results concerning periodic local minimizers of the area functional and a proof, via second variation, of the sharp quantitative isoperimetric inequality in the standard Euclidean case. As a further application, we address the global and local minimality of certain lamellar configurations.

Keywords

Diblock Copolymer Volume Constraint Periodic Case Isoperimetric Problem Nonlocal Term 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità Degli Studi di ParmaParmaItaly
  2. 2.Dipartimento di Matematica e Applicazioni “R. Caccioppoli”Università Degli Studi di Napoli “Federico II”NapoliItaly

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