Title

Korn's Inequality and Eigenproblems for the Lame Operator

Published In

Computational Methods in Applied Mathematics

Document Type

Citation

Publication Date

3-17-2022

Abstract

In this paper, we show that the so-called Korn inequality holds for vector fields with a zero normal or tangential trace on a subset (of positive measure) of the boundary of Lipschitz domains. We further show that the validity of this inequality depends on the geometry of this subset of the boundary. We then consider three eigenvalue problems for the Lamé operator: we constrain the traction in the tangential direction and the normal component of the displacement, the related problem of constraining the normal component of the traction and the tangential component of the displacement, and a third eigenproblem that considers mixed boundary conditions. We show that eigenpairs for these eigenproblems exist on a broad variety of domains. Analytic solutions for some of these eigenproblems are given on simple domains.

Rights

© 2022 Walter de Gruyter GmbH, Berlin/Boston

DOI

10.1515/cmam-2021-0144

Persistent Identifier

https://archives.pdx.edu/ds/psu/37377

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