Korn's inequality in anisotropic Sobolev spaces

Korn's inequality has been at the heart of much exciting research since its first appearance in the beginning of the 20th century. Many are the applications of this inequality to the analysis and construction of discretizations of a large variety of problems in continuum mechanics. In this pape...

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Bibliographic Details
Published in:arXiv.org 2022-12
Main Authors: Benavides, Gonzalo A, Domínguez-Rivera, Sebastián A
Format: Article
Language:English
Subjects:
Continuum mechanics
Sobolev space
Online Access:Get full text
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Summary:Korn's inequality has been at the heart of much exciting research since its first appearance in the beginning of the 20th century. Many are the applications of this inequality to the analysis and construction of discretizations of a large variety of problems in continuum mechanics. In this paper, we prove that the classical Korn inequality holds true in {\it anisotropic Sobolev spaces}. We also prove that an extension of Korn's inequality, involving non-linear continuous maps, is valid in such spaces. Finally, we point out that another classical inequality, Poincare's inequality, also holds in anisotropic Sobolev spaces.
ISSN:2331-8422
DOI:10.48550/arxiv.2212.00874