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.
DOI : 10.1051/cocv/2014031
Mots clés : Nonlocal isoperimetric problem, sphere, axisymmetric critical points, self-assembly of diblock copolymers
@article{COCV_2015__21_1_247_0,
author = {Choksi, Rustum and Topaloglu, Ihsan and Tsogtgerel, Gantumur},
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},
volume = {21},
number = {1},
year = {2015},
doi = {10.1051/cocv/2014031},
zbl = {1319.35307},
mrnumber = {3348422},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2014031/}
}
TY - JOUR AU - Choksi, Rustum AU - Topaloglu, Ihsan AU - Tsogtgerel, Gantumur TI - Axisymmetric critical points of a nonlocal isoperimetric problem on the two-sphere JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2015 SP - 247 EP - 270 VL - 21 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2014031/ DO - 10.1051/cocv/2014031 LA - en ID - COCV_2015__21_1_247_0 ER -
%0 Journal Article %A Choksi, Rustum %A Topaloglu, Ihsan %A Tsogtgerel, Gantumur %T Axisymmetric critical points of a nonlocal isoperimetric problem on the two-sphere %J ESAIM: Control, Optimisation and Calculus of Variations %D 2015 %P 247-270 %V 21 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2014031/ %R 10.1051/cocv/2014031 %G en %F COCV_2015__21_1_247_0
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://www.numdam.org/articles/10.1051/cocv/2014031/
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