Interfaces and Free Boundaries
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On the global minimizers of a nonlocal isoperimetric problem in two dimensionsPeter Sternberg and Ihsan Topaloglu (1) Department of Mathematics, Indiana University, IN 47405, BLOOMINGTON, UNITED STATES
(2) Department of Mathematics and Statistics, McMaster University, L8S 4K1, HAMILTON, ONTARIO, CANADA
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.
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Sternberg Peter, Topaloglu Ihsan: On the global minimizers of a nonlocal isoperimetric problem in two dimensions. Interfaces Free Bound. 13 (2011), 155-169. doi: 10.4171/IFB/252