Jump to ContentJump to Main Navigation
Gamma-Convergence for Beginners$
Users without a subscription are not able to see the full content.

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

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2019. All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a monograph in OSO for personal use (for details see www.oxfordscholarship.com/page/privacy-policy).date: 23 May 2019

*SOME COMMENTS ON VECTORIAL PROBLEMS

*SOME COMMENTS ON VECTORIAL PROBLEMS

Chapter:
(p.161) 12 *SOME COMMENTS ON VECTORIAL PROBLEMS
Source:
Gamma-Convergence for Beginners
Author(s):

Andrea Braides

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198507840.003.0013

This chapter shows that some notions used in a one-dimensional setting can be extended to higher dimensions and vector problems if properly modified. In particular, convexity requirements for lower semicontinuity lead to the notions of quasiconvexity and polyconvexity, and homogenization formulas are proven to hold in a vector setting once the cell-problem formula is discarded, being valid only in a convex setting. New phenomena arise that are not meaningful in one dimension, as the instability of polyconvexity by homogenization and the density of isotropic quadratic functionals in all quadratic forms.

Keywords:   vector problems, quasiconvexity, polyconvexity, homogenization formulas, instability of polyconvexity, quadratic forms, density

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .