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

Peter Sternberg | Zendy; Ihsan Topaloglu | Zendy

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

Author(s) -

Peter Sternberg,

Ihsan Topaloglu

Publication year - 2011

Publication title -

interfaces and free boundaries mathematical analysis computation and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.964

H-Index - 39

eISSN - 1463-9971

pISSN - 1463-9963

DOI - 10.4171/ifb/252

Subject(s) - isoperimetric inequality , mathematics , boundary (topology) , torus , constraint (computer aided design) , interval (graph theory) , quantum nonlocality , mathematical analysis , boundary value problem , physics , geometry , combinatorics , quantum mechanics , quantum entanglement , quantum

In this article 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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