Closure and commutability results for Gamma-limits and the geometric linearization and homogenization of multi-well energy functionals

Under a suitable notion of equivalence of integral densities we prove a \(\Gamma\)-closure theorem for integral functionals: The limit of a sequence of \(\Gamma\)-convergent families of such functionals is again a \(\Gamma\)-convergent family. Its \(\Gamma\)-limit is the limit of the \(\Gamma\)-limi...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Authors Jesenko, Martin, Schmidt, Bernd
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 05.08.2013
Subjects
Convergence
Elasticity
Homogenization
Integrals
Linearization
Mathematics - Analysis of PDEs
Mathematics - Functional Analysis
Physics - Materials Science
Online AccessGet full text

Cover

More Information
Summary:Under a suitable notion of equivalence of integral densities we prove a \(\Gamma\)-closure theorem for integral functionals: The limit of a sequence of \(\Gamma\)-convergent families of such functionals is again a \(\Gamma\)-convergent family. Its \(\Gamma\)-limit is the limit of the \(\Gamma\)-limits of the original problems. This result not only provides a common basic principle for a number of linearization and homogenization results in elasticity theory. It also allows for new applications as we exemplify by proving that geometric linearization and homogenization of multi-well energy functionals commute.
ISSN:2331-8422
DOI:10.48550/arxiv.1308.0963