Generalized Korn's inequality and conformal Killing vectors

Details Generalized Korn's inequality and conformal Killing vectors Generalized Korn's inequality and conformal Killing vectors

2005-05-04

arxiv.org/abs/gr-qc/0505022v1

Calc.Var.Part.Differ.Equ.25:535-540, 2006

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

8 pages

Scientific paper

10.1007/s00526-005-0371-4

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.

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