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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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INTEGRAL PROBLEMS

INTEGRAL PROBLEMS

Chapter:
(p.40) 2 INTEGRAL PROBLEMS
Source:
Gamma-Convergence for Beginners
Author(s):

Andrea Braides

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198507840.003.0003

This chapter deals with integral problems. Using examples, it illustrates the need to use weak topologies to obtain compactness and coerciveness conditions. The sufficiency and necessity of the convexity of integrands is proved. A characterization of Gamma-convergence in terms of convex analysis is given. The result is extended to Sobolev spaces, where the problem of dealing with boundary values is introduced. Examples of degenerate integrals with limits defined on discontinuous functions or by functions of the sup-norm are given.

Keywords:   integral functionals, weak topologies, Sobolev spaces, Convex Analysis, boundary value problems, degenerate integral functionals

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