Paper Info
Title
Lower Semicontinuity of Quasi-convex Bulk Energies in SBV and Integral Representation in Dimension Reduction
Abstract
A result of Larsen concerning the structure of the approximate gradient of certain sequences of functions with bounded variation is used to present a short proof of Ambrosio's lower semicontinuity theorem for quasi-convex bulk energies in SBV. It enables us to generalize to the SBV setting the decomposition lemma for scaled gradients in dimension reduction and also to show that, from the point of view of bulk energies, SBV dimensional reduction problems can be reduced to analog ones in the Sobolev spaces framework.
Year
DOI
Venue
2008
10.1137/060676416
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Keywords
Field
DocType
dimension reduction,Gamma-convergence,functions of bounded variation,free discontinuity problems,quasi convexity,equi-integrability
Mathematical analysis,Discontinuity (linguistics),Sobolev space,Regular polygon,Decomposition method (constraint satisfaction),Γ-convergence,Dimensional reduction,Bounded variation,Lemma (mathematics),Mathematics
Journal
Volume
Issue
ISSN
39
6
0036-1410
Citations 
PageRank 
References 
0
0.34
0
Authors
1
Name
Order
Citations
PageRank
Jean-François Babadjian121.49