Generalized Korn's inequality and conformal Killing vectors
General Relativity and Quantum Cosmology
2009-12-04 v1
Abstract
Korn's inequality plays an important role in linear elasticity theory. This inequality bounds the norm of the derivatives of the displacement vector by the norm of the linearized strain tensor. The kernel of the linearized strain tensor are the infinitesimal rigid-body translations and rotations (Killing vectors). We generalize this inequality by replacing the linearized strain tensor by its trace free part. That is, we obtain a stronger inequality in which the kernel of the relevant operator are the conformal Killing vectors. The new inequality has applications in General Relativity.
Cite
@article{arxiv.gr-qc/0505022,
title = {Generalized Korn's inequality and conformal Killing vectors},
author = {Sergio Dain},
journal= {arXiv preprint arXiv:gr-qc/0505022},
year = {2009}
}
Comments
8 pages