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We show that in a two-dimensional bounded open set whose complement has a finite number of connected components, the vector fieldsuH1(Ωℝ2) are dense in the space of fields whose symmetrized gradiente(u) is inL2(Ωℝ4). This allows us to show the continuity of some linearized elasticity problems with respect to variations of the set, with applications to shape optimization or the study of crack evolution.
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CEREMADE (CNRS UMR 7534), Université de Paris-Dauphine, place de Lattre de Tassigny, 75775 Paris CEDEX 16, France. e-mail: antonin.chambolle@ceremade.dauphine.fr, , , , , , FR
Antonin Chambolle
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(Accepted September 18, 2002)Published online February 4, 2003
Commmunicated by V. Šverák
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Chambolle, A. A Density Result in Two-Dimensional Linearized Elasticity, and Applications.Arch. Rational Mech. Anal.167, 211–233 (2003). https://doi.org/10.1007/s00205-002-0240-7
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