Displaying similar documents to “Linear convergence in the approximation of rank-one convex envelopes”

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

Krzysztof Chełmiński, Agnieszka Kałamajska (2006)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider the lower semicontinuous functional of the form I f ( u ) = Ω f ( u ) 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...

An approximation theorem for sequences of linear strains and its applications

Kewei Zhang (2004)

ESAIM: Control, Optimisation and Calculus of Variations

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We establish an approximation theorem for a sequence of linear elastic strains approaching a compact set in L 1 by the sequence of linear strains of mapping bounded in Sobolev space W 1 , p . We apply this result to establish equalities for semiconvex envelopes for functions defined on linear strains via a construction of quasiconvex functions with linear growth.

A note on equality of functional envelopes

Martin Kružík (2003)

Mathematica Bohemica

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We characterize generalized extreme points of compact convex sets. In particular, we show that if the polyconvex hull is convex in m × n , min ( m , n ) 2 , then it is constructed from polyconvex extreme points via sequential lamination. Further, we give theorems ensuring equality of the quasiconvex (polyconvex) and the rank-1 convex envelopes of a lower semicontinuous function without explicit convexity assumptions on the quasiconvex (polyconvex) envelope.