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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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*AN INTRODUCTION TO THE LOCALIZATION METHOD OF Γ-CONVERGENCE

*AN INTRODUCTION TO THE LOCALIZATION METHOD OF Γ-CONVERGENCE

Chapter:
(p.194) 16 *AN INTRODUCTION TO THE LOCALIZATION METHOD OF Γ-CONVERGENCE
Source:
Gamma-Convergence for Beginners
Author(s):

Andrea Braides

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198507840.003.0017

This chapter provides an introduction to the localization method of Gamma-convergence. It presents a brief account of the localization methods of Gamma-convergence that allows for the proof of general compactness theorems when direct characterizations are not available: energies are localized on open sets, where Gamma-limits indexed by the set are proved to exist defining a set function; subadditivity and regularity properties of this set function ensure that it is a measure by the De Giorgi-Letta measure criterion; integral representation theorems allow to give a description of the Gamma-limit.

Keywords:   localization methods, compactness theorems, set functions, De Giorgi-Letta measure criterion, integral representation

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