An approximation theorem for sequences of linear strains and its applications

Zhang, Kewei

ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 2, pp. 224-242.

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.

Classification : 26B25, 41A30, 49J45
Mots clés : linear strains, maximal function, approximate sequences, quasiconvex envelope, quasiconvex hull

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