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Gamma-Convergence for Beginners$
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Andrea Braides

Print publication date: 2002

Print ISBN-13: 9780198507840

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198507840.001.0001

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*THE ‘SLICING’ METHOD

*THE ‘SLICING’ METHOD

Chapter:
(p.187) 15*THE ‘SLICING’ METHOD
Source:
Gamma-Convergence for Beginners
Author(s):

Andrea Braides

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198507840.003.0016

This chapter presents a self-contained account of the slicing method that allows the exhibition of a lower bound for high-dimensional problems through their one-dimensional sections. After computing a family of one-dimensional limit problems, an optimization is performed through an argument characterizing the supremum of a family of measures. The upper inequality is obtained by a density argument whenever recovery sequences have a one-dimensional form. This method can be applied to the high-dimensional gradient theory of phase transitions.

Keywords:   one-dimensional sections, supremum of measures, density argument, phase transitions

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