BMO and Elasticity: Korn’s Inequality; Local Uniqueness in Tension
| Autor: | Scott J. Spector, Daniel Spector |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Finite elasticity
BMO local minimizers Mathematics::Analysis of PDEs Mathematics::Classical Analysis and ODEs Nonlinear elasticity 02 engineering and technology Positive-definite matrix Bounded mean oscillation 01 natural sciences 0203 mechanical engineering General Materials Science Uniqueness 0101 mathematics Elasticity (economics) Mathematics Mathematics::Functional Analysis Mechanical Engineering Mathematical analysis Linear elasticity Function (mathematics) Small strains 010101 applied mathematics 020303 mechanical engineering & transports Korn's inequality Mechanics of Materials Equilibrium solutions Constant (mathematics) Korn’s inequality |
| Zdroj: | Journal of Elasticity. 143(1):85-109 |
| ISSN: | 0374-3535 |
| DOI: | 10.1007/s10659-020-09805-5 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink