Geodesic
Axisymmetric critical points of a nonlocal isoperimetric problem on the two-sphere
Choksi, Rustum1  ; Topaloglu, Ihsan1 ; Tsogtgerel, Gantumur1
1 Deparment of Mathematics and Statistics, McGill University, Montréal, Québec, H3A 0B9, Canada.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 1, pp. 247-270

Voir la notice de l'article provenant de la source Numdam

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
Keywords: 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. 
@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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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

Cité par Sources :