Korn’s inequality in anisotropic Sobolev spaces

Author:

Benavides Gonzalo A.1ORCID,Domínguez-Rivera Sebastián A.2ORCID

Affiliation:

1. Department of Mathematics , University of Maryland , College Park , MD 20742 , USA

2. Department of Mathematics and Statistics , University of Saskatchewan , Saskatoon , Canada

Abstract

Abstract 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 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, namely Poincaré’s inequality, also holds in anisotropic Sobolev spaces.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Theory and Mathematics,Statistics, Probability and Uncertainty,Mathematical Physics

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