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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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INTRODUCTION

INTRODUCTION

Chapter:
(p.1) INTRODUCTION
Source:
Gamma-Convergence for Beginners
Author(s):

Andrea Braides

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198507840.003.0001

The idea of a variational convergence is introduced as an equality of upper and lower bounds for families of variational problems. Examples are given that illustrate some of the main applications of Gamma-convergence, starting from the gradient theory of phase transitions, through homogenization and dimension reduction, to limits of atomistic theories. A final section shows how the definition of Gamma-convergence can be deduced from the requirement that it implies the convergence of minimizers be local and stable under continuous perturbations.

Keywords:   variational convergence, upper bounds, lower bounds, phase transitions, homogenization, dimension reduction, atomistic theories, direct methods

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