On the optimal constants in Korn's and geometric rigidity estimates, in bounded and unbounded domains, under Neumann boundary conditions
Abstract
We are concerned with the optimal constants: in the Korn inequality under tangential boundary conditions on bounded sets $\Omega \subset \mathbb{R}^n$, and in the geometric rigidity estimate on the whole $\mathbb{R}^2$. We prove that the latter constant equals $\sqrt{2}$, and we discuss the relation of the former constants with the optimal Korn's constants under Dirichlet boundary conditions, and in the whole $\mathbb{R}^n$, which are well known to equal $\sqrt{2}$. We also discuss the attainability of these constants and the structure of deformations/displacement fields in the optimal sets.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2015
- DOI:
- 10.48550/arXiv.1501.01917
- arXiv:
- arXiv:1501.01917
- Bibcode:
- 2015arXiv150101917L
- Keywords:
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- Mathematics - Analysis of PDEs