, Volume 75, Issue 1, pp 7-21

Functions of bounded deformation

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Abstract

We study the space BD(Ω), composed of vector functions u for which all components εij=1/2(u i, j+u j, i) of the deformation tensor are bounded measures. This seems to be the correct space for the displacement field in the problems of perfect plasticity. We prove that the boundary values of every such u are integrable; indeed their trace is in L 1 (Γ)N. We show also that if a distribution u yields ɛ ij which are measures, then u must lie in L p(Ω) for p≦N/(N−1).

The second author gratefully acknowledges the supprot of the National Science Foundation.