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Local and global minimality results for an isoperimetric problem with long-range interactions

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Free Discontinuity Problems

Part of the book series: Publications of the Scuola Normale Superiore ((CRMSNS,volume 19))

Abstract

In this paper we review some recent results concerning the following non-local isoperimetric problem:

where m ∈ (-1,1) is given and prescribes the volume of the two phases {u = 1} and {u = -1}. Here PΩ stands for the perimeter relative to Ω (in the sense of Caccioppoli-De Giorgi) and BV(Ω; {-1, 1}) denotes the space of functions of bounded variation taking values in {-1, 1}. We refer to [4] and [33] for a rather complete account on the properties of functions of bounded variations and sets of finite perimeter.

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Authors
  1. Massimiliano Morini
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Nicola Fusco Aldo Pratelli

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Morini, M. (2016). Local and global minimality results for an isoperimetric problem with long-range interactions. In: Fusco, N., Pratelli, A. (eds) Free Discontinuity Problems. Publications of the Scuola Normale Superiore, vol 19. Edizioni della Normale, Pisa. https://doi.org/10.1007/978-88-7642-593-6_3

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