JournalsifbVol. 13, No. 1pp. 155–169

On the global minimizers of a nonlocal isoperimetric problem in two dimensions

  • Peter Sternberg

    Indiana University, Bloomington, United States
  • Ihsan Topaloglu

    McMaster University, Hamilton, Canada
On the global minimizers of a nonlocal isoperimetric problem in two dimensions cover
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Abstract

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.

Cite this article

Peter Sternberg, Ihsan Topaloglu, On the global minimizers of a nonlocal isoperimetric problem in two dimensions. Interfaces Free Bound. 13 (2011), no. 1, pp. 155–169

DOI 10.4171/IFB/252