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arXiv · 1301.7213

Minimality via second variation for microphase separation of diblock copolymer melts

Vesa Julin·Giovanni Pisante
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Abstract

We consider a non local isoperimetric problem arising as the sharp interface limit of the Ohta-Kawasaki free energy introduced to model microphase separation of diblock copolymers. We perform a second order variational analysis that allows us to provide a quantitative second order minimality condition. We show that critical configurations with positive second variation are indeed strict local minimizers of the nonlocal perimeter. Moreover we provide, via a suitable quantitative inequality of isoperimetric type, an estimate of the deviation from minimality for configurations close to the minimum in the $L^1$ topology .

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Vesa Julin, Giovanni Pisante. 2013-01-30. Minimality via second variation for microphase separation of diblock copolymer melts. https://arxiv.org/abs/1301.7213

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