On global minimizers for a variational problem with long-range interactions

Choksi, Rustum

doi:10.1090/S0033-569X-2012-01316-9

Author: Rustum Choksi
Journal: Quart. Appl. Math. 70 (2012), 517-537
MSC (2010): Primary 49S05; Secondary 49M30, 35K30, 35K55, 74N15
DOI: https://doi.org/10.1090/S0033-569X-2012-01316-9
Published electronically: May 24, 2012
MathSciNet review: 2986133
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Abstract: Energy-driven pattern formation induced by competing short and long-range interactions is common in many physical systems. In these proceedings we report on certain rigorous asymptotic results concerning global minimizers of a nonlocal perturbation to the well-known Ginzburg-Landau/Cahn-Hilliard free energy. We also discuss two hybrid numerical methods for accessing the ground states of these functionals.

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