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An approximation theorem for sequences of linear strains and its applications
2004
E S A I M: 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. Mathematics Subject Classification. 26B25, 41A30, 49J45. R n |e(Dv k )| p dx ≤ C(n, p) < +∞, and lim k→∞ Ω |e(Du j k ) − e(Dv k )|dx = 0. (1.2)
doi:10.1051/cocv:2004001
fatcat:gu7oom7woralvjco4vqyavktt4