We analyze the minimization of a nonlocal isoperimetric problem (NLIP) posed on the flat 2-torus. After establishing regularity of the free boundary of minimizers, we show that when the parameter controlling the influence of the nonlocality is small, there is an interval of values for the mass constraint such that the global minimizer is exactly lamellar, that is, the free boundary consists of two parallel lines. In other words, in this parameter regime, the global minimizer of the 2d (NLIP) coincides with the global minimizer of the local periodic isoperimetric problem.
1
Indiana University, Bloomington, United States
2
McMaster University, Hamilton, Canada
Peter Sternberg; Ihsan Topaloglu. On the global minimizers of a nonlocal isoperimetric problem in two dimensions. Interfaces and free boundaries, Tome 13 (2011) no. 1, pp. 155-169. doi: 10.4171/ifb/252
@article{10_4171_ifb_252,
author = {Peter Sternberg and Ihsan Topaloglu},
title = {On the global minimizers of a nonlocal isoperimetric problem in two dimensions},
journal = {Interfaces and free boundaries},
pages = {155--169},
year = {2011},
volume = {13},
number = {1},
doi = {10.4171/ifb/252},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/252/}
}
TY - JOUR
AU - Peter Sternberg
AU - Ihsan Topaloglu
TI - On the global minimizers of a nonlocal isoperimetric problem in two dimensions
JO - Interfaces and free boundaries
PY - 2011
SP - 155
EP - 169
VL - 13
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.4171/ifb/252/
DO - 10.4171/ifb/252
ID - 10_4171_ifb_252
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%A Ihsan Topaloglu
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%J Interfaces and free boundaries
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%P 155-169
%V 13
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%U http://geodesic.mathdoc.fr/articles/10.4171/ifb/252/
%R 10.4171/ifb/252
%F 10_4171_ifb_252
