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Issue ESAIM: COCV
Volume 10, Number 2, April 2004
Page(s) 224 - 242
DOI 10.1051/cocv:2004001

ESAIM: COCV, April 2004, Vol. 10, pp. 224-242
DOI: 10.1051/cocv:2004001

An approximation theorem for sequences of linear strains and its applications

Kewei Zhang

School of Mathematical Sciences, University of Sussex Brighton, BN1 9QH, UK; k.zhang@sussex.ac.uk.


(Received July 4, 2002. Revised September 22, 2003.)

Abstract
We establish an approximation theorem for a sequence of linear elastic strains approaching a compact set in L1 by the sequence of linear strains of mapping bounded in Sobolev space W1,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.


Mathematics Subject Classification. 26B25, 41A30, 49J45.

Key words: Linear strains, maximal function, approximate sequences, quasiconvex envelope, quasiconvex hull.


© EDP Sciences, SMAI 2004


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