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New convexity conditions in the calculus of variations and compensated compactness theory
Published online by Cambridge University Press: 15 December 2005
Abstract
We consider the lower semicontinuous functional of the form
$I_f(u)=\int_\Omega f(u){\rm d}x$ where u satisfies a given
conservation law defined by differential operator of degree one
with constant coefficients. We show that under certain constraints
the well known Murat and Tartar's Λ-convexity condition
for the integrand f extends to the new geometric conditions
satisfied on four dimensional symplexes. Similar conditions on
three dimensional symplexes were recently obtained by the second
author. New conditions apply to quasiconvex functions.
- Type
- Research Article
- Information
- ESAIM: Control, Optimisation and Calculus of Variations , Volume 12 , Issue 1 , January 2006 , pp. 64 - 92
- Copyright
- © EDP Sciences, SMAI, 2006
References
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