# New convexity conditions in the calculus of variations and compensated compactness theory

Krzysztof Chełmiński; Agnieszka Kałamajska

ESAIM: Control, Optimisation and Calculus of Variations (2005)

- Volume: 12, Issue: 1, page 64-92
- ISSN: 1292-8119

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topChełmiński, Krzysztof, and Kałamajska, Agnieszka. "New convexity conditions in the calculus of variations and compensated compactness theory." ESAIM: Control, Optimisation and Calculus of Variations 12.1 (2005): 64-92. <http://eudml.org/doc/90791>.

@article{Chełmiński2005,

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.
},

author = {Chełmiński, Krzysztof, Kałamajska, Agnieszka},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Quasiconvexity; rank-one convexity; semicontinuity.; semicontinuity},

language = {eng},

month = {12},

number = {1},

pages = {64-92},

publisher = {EDP Sciences},

title = {New convexity conditions in the calculus of variations and compensated compactness theory},

url = {http://eudml.org/doc/90791},

volume = {12},

year = {2005},

}

TY - JOUR

AU - Chełmiński, Krzysztof

AU - Kałamajska, Agnieszka

TI - New convexity conditions in the calculus of variations and compensated compactness theory

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2005/12//

PB - EDP Sciences

VL - 12

IS - 1

SP - 64

EP - 92

AB -
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.

LA - eng

KW - Quasiconvexity; rank-one convexity; semicontinuity.; semicontinuity

UR - http://eudml.org/doc/90791

ER -

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