6533b873fe1ef96bd12d591a
RESEARCH PRODUCT
Minimality via second variation for microphase separation of diblock copolymer melts
Vesa JulinGiovanni Pisantesubject
49Q10isoperimetric problemsApplied MathematicsGeneral Mathematics010102 general mathematicsSeparation (aeronautics)Mathematical analysisOrder (ring theory)Type (model theory)01 natural sciences010101 applied mathematicsMathematics - Analysis of PDEsinterfacial problemsFOS: MathematicsCopolymercopolymersLimit (mathematics)0101 mathematicsVariational analysisIsoperimetric inequalityTopology (chemistry)Analysis of PDEs (math.AP)Mathematicsdescription
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 problem. 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 {L^{1}} -topology.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-01-01 |