Isoperimetric Problems Between Analysis and Geometry

Stability and minimality for a nonlocal variational problem

Nicola Fusco (Dip. Mat. Univ. Napoli)

created by paolini on 02 Jun 2014
modified on 03 Jun 2014

17 jun 2014 -- 09:30   [open in google calendar]


I will discuss the local minimality of certain configurations for a nonlocal isoperimetric problem used to model microphase separation in diblock copolymer melts. I will 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 close in $L^1$. As a byproduct of the quantitative estimate, one gets new results concerning periodic minimal surfaces and the global and local minimality of certain configurations.