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ERC Workshop on Geometric Partial Differential Equations

Minimality Via Second Variation for a Non-Local Isoperimetric Problem

speaker: Massimiliano Morini (Università di Parma)

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 $L1$-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.

Thu 13 Sep, 15:45 - 16:30, Aula Magna Dipartimento di Matematica
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