Axisymmetric critical points of a nonlocal isoperimetric problem on the two-sphere
ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 1, pp. 247-270.

On the two dimensional sphere, we consider axisymmetric critical points of an isoperimetric problem perturbed by a long-range interaction term. When the parameter controlling the nonlocal term is sufficiently large, we prove the existence of a local minimizer with arbitrary many interfaces in the axisymmetric class of admissible functions. These local minimizers in this restricted class are shown to be critical points in the broader sense (i.e., with respect to all perturbations). We then explore the rigidity, due to curvature effects, in the criticality condition via several quantitative results regarding the axisymmetric critical points.

Reçu le :
DOI : 10.1051/cocv/2014031
Classification : 35R35, 49Q20, 74N15, 82B26, 82D60
Mots clés : Nonlocal isoperimetric problem, sphere, axisymmetric critical points, self-assembly of diblock copolymers
Choksi, Rustum 1 ; Topaloglu, Ihsan 1 ; Tsogtgerel, Gantumur 1

1 Deparment of Mathematics and Statistics, McGill University, Montréal, Québec, H3A 0B9, Canada.
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     title = {Axisymmetric critical points of a nonlocal isoperimetric problem on the two-sphere},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {247--270},
     publisher = {EDP-Sciences},
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Choksi, Rustum; Topaloglu, Ihsan; Tsogtgerel, Gantumur. Axisymmetric critical points of a nonlocal isoperimetric problem on the two-sphere. ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 1, pp. 247-270. doi : 10.1051/cocv/2014031. http://archive.numdam.org/articles/10.1051/cocv/2014031/

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