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Journal Article

Generalized Korn's inequality and conformal Killing vectors

MPS-Authors

Dain,  Sergio
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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cvpda535.pdf
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Citation

Dain, S. (2006). Generalized Korn's inequality and conformal Killing vectors. Calculus of Variations and Partial Differential Equations, 25(4), 535-540.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-4A75-6
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.