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linear strains

ESAIM: Control, Optimisation and Calculus of Variations (1)

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An approximation theorem for sequences of linear strains and its applications
Kewei Zhang
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 10 / Issue 2 / April 2004

Published online by Cambridge University Press:

15 March 2004, pp. 224-242

Print publication:

April 2004
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We establish an approximation theorem for a sequence oflinear elastic strains approaching a compact set in L 1 by thesequence of linear strains of mapping bounded in Sobolev space W 1,p . We apply this result to establish equalities forsemiconvex envelopes for functions defined on linear strains via a construction of quasiconvex functions with linear growth.