JOURNAL ARTICLE

Korn's inequality in anisotropic Sobolev spaces.

  • Published In: Journal of Applied Analysis, 2023, v. 29, n. 2. P. 367 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: Benavides, Gonzalo A.; Domínguez-Rivera, Sebastián A. 3 of 3

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. [ABSTRACT FROM AUTHOR]

Additional Information

  • Source:Journal of Applied Analysis. 2023/12, Vol. 29, Issue 2, p367
  • Document Type:Article
  • Subject Area:Physics
  • Publication Date:2023
  • ISSN:1425-6908
  • DOI:10.1515/jaa-2023-0031
  • Accession Number:173777208
  • Copyright Statement:Copyright of Journal of Applied Analysis is the property of De Gruyter and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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