BMO and Elasticity: Korn’s Inequality; Local Uniqueness in Tension

Daniel E. Spector, Scott J. Spector*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

In this manuscript two BMO estimates are obtained, one for Linear Elasticity and one for Nonlinear Elasticity. It is first shown that the BMO-seminorm of the gradient of a vector-valued mapping is bounded above by a constant times the BMO-seminorm of the symmetric part of its gradient, that is, a Korn inequality in BMO. The uniqueness of equilibrium for a finite deformation whose principal stresses are everywhere nonnegative is then considered. It is shown that when the second variation of the energy, when considered as a function of the strain, is uniformly positive definite at such an equilibrium solution, then there is a BMO-neighborhood in strain space where there are no other equilibrium solutions.

Original languageEnglish
Pages (from-to)85-109
Number of pages25
JournalJournal of Elasticity
Volume143
Issue number1
DOIs
Publication statusPublished - 2021 Jan
Externally publishedYes

Keywords

  • BMO local minimizers
  • Bounded mean oscillation
  • Equilibrium solutions
  • Finite elasticity
  • Korn’s inequality
  • Nonlinear elasticity
  • Small strains
  • Uniqueness

ASJC Scopus subject areas

  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering

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