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BMO and Elasticity: Korn’s Inequality; Local Uniqueness in Tension
- Source :
- Journal of Elasticity. 143(1):85-109
- Publication Year :
- 2021
- Publisher :
- Springer Nature, 2021.
-
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.
- Subjects :
- 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
Subjects
Details
- Language :
- English
- ISSN :
- 03743535
- Volume :
- 143
- Issue :
- 1
- Database :
- OpenAIRE
- Journal :
- Journal of Elasticity
- Accession number :
- edsair.doi.dedup.....aad7e41fe1381936ec25c35cf0e7ee33