Archive for Rational Mechanics and Analysis

, Volume 75, Issue 1, pp 7–21

Functions of bounded deformation

  • Roger Temam
  • Gilbert Strang
Article

DOI: 10.1007/BF00284617

Cite this article as:
Temam, R. & Strang, G. Arch. Rational Mech. Anal. (1980) 75: 7. doi:10.1007/BF00284617

Abstract

We study the space BD(Ω), composed of vector functions u for which all components εij=1/2(ui, j+uj, 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 L1 (Γ)N. We show also that if a distribution u yields ɛij which are measures, then u must lie in Lp(Ω) for p≦N/(N−1).

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Roger Temam
    • 1
    • 2
  • Gilbert Strang
    • 1
    • 2
  1. 1.Laboratoire d'Analyse NumériqueUniversité de Paris-SudOrsay
  2. 2.Department of MathematicsMassachusetts Institute of TechnologyUSA

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