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RESEARCH PRODUCT

Remark on a nonlocal isoperimetric problem

Vesa Julin

subject

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)Mathematics

description

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.

yearjournalcountryeditionlanguage
2017-05-01Nonlinear Analysis: Theory, Methods and Applications
10.1016/j.na.2016.10.011https://doi.org/10.1016/j.na.2016.10.011