Korn's Inequality and Eigenproblems for the Lame Operator
Sponsor
National Science Foundation Award Identifier / Grant number: DMS-2012285.
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
Locate the Document
DOI
10.1515/cmam-2021-0144
Persistent Identifier
https://archives.pdx.edu/ds/psu/37377
Citation Details
Domínguez-Rivera, S. A., Nigam, N., & Ovall, J. S. (2022). Korn’s Inequality and Eigenproblems for the Lamé Operator. Computational Methods in Applied Mathematics.