ESAIM: Control, Optimisation and Calculus of Variations

Table of Contents - April 2004 - Volume 10, Issue 02  

Research Article

An approximation theorem for sequences of linear strains and its applications

Zhang, Kewei

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

Abstract

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.

(Received July 4 2002)

(Revised September 22 2003)

(Online publication March 15 2004)

Key Words:

  • Linear strains;
  • maximal function;
  • approximate sequences;
  • quasiconvex envelope;
  • quasiconvex hull.

Mathematics Subject Classification:

  • 26B25;
  • 41A30;
  • 49J45