Stability and minimality for a nonlocal variational problem
Nicola Fusco (Dip. Mat. Univ. Napoli)
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.