## 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 language | English |
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Pages (from-to) | 85-109 |

Number of pages | 25 |

Journal | Journal of Elasticity |

Volume | 143 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2021 Jan |

Externally published | Yes |

## 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