Search results for "isoperimetric problem"

showing 2 items of 2 documents

Minimality via second variation for microphase separation of diblock copolymer melts

2017

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.

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)Mathematics
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Remark on a nonlocal isoperimetric problem

2017

Abstract We consider isoperimetric problem with a nonlocal repulsive term given by the Newtonian potential. We prove that regular critical sets of the functional are analytic. This optimal regularity holds also for critical sets of the Ohta–Kawasaki functional. We also prove that when the strength of the nonlocal part is small the ball is the only possible stable critical set.

Newtonian potentialcritical pointsApplied Mathematics010102 general mathematicsMathematical analysista111Isoperimetric dimension01 natural sciences010101 applied mathematicsMathematics - Analysis of PDEsshape optimizationFOS: Mathematicsisoperimetric problemShape optimizationBall (mathematics)0101 mathematicsIsoperimetric inequalityAnalysisCritical setAnalysis of PDEs (math.AP)MathematicsNonlinear Analysis: Theory, Methods and Applications
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