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Divergence Operator and Related Inequalities

  • Book
  • © 2017


  • Unified and self-contained presentation of fundamental tools in continuum mechanics
  • Provides a constructive and descriptive approach to the mathematical framework with a growing level of complexity
  • Numerous connections between different topics are included to appeal to a wide audience
  • Includes supplementary material:

Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)

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Table of contents (4 chapters)


About this book

This Brief is mainly devoted to two classical and related results: the existence of a right inverse of the divergence operator and the so-called Korn Inequalities. It is well known that both results are fundamental tools in the analysis of some classic differential equations, particularly in those arising in fluid dynamics and elasticity. Several connections between these two topics and improved Poincaré inequalities are extensively treated. From simple key ideas the book is growing smoothly in complexity. Beginning with the study of these problems on star-shaped domains the arguments are extended first to John domains and then to Hölder  α domains where the need of weighted spaces arises naturally. In this fashion, the authors succeed in presenting in an unified and concise way several classic and recent developments in the field. These features certainly makes this Brief useful for students, post-graduate students, and researchers as well.


“This book is a very nice introduction to many central topics in PDEs regarding the existence of a right inverse of the divergence operator divp, which is strongly related to the Korn inequality, Stokes equation, etc. … These features certainly make this Springer Briefs manuscript very useful for students, postgraduate students, and researchers as well. (Javier Soria, zbMATH 1394.35001, 2018)

“This book gives a detailed discussion of two basic inequalities that are of fundamental importance in a variety of fields and discusses how their validity connects to geometric properties of the underlying domain. … The book is nicely written, hints at open problems and is supplemented withmany informative figures.” (Stefan Steinerberger, Mathematical Reviews, October, 2017)

Authors and Affiliations

  • Department of Mathematics and IMAS, University of Buenos Aires and CONICET, Buenos Aires, Argentina

    Gabriel Acosta, Ricardo G. Durán

Bibliographic Information

  • Book Title: Divergence Operator and Related Inequalities

  • Authors: Gabriel Acosta, Ricardo G. Durán

  • Series Title: SpringerBriefs in Mathematics

  • DOI:

  • Publisher: Springer New York, NY

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Author(s) 2017

  • Softcover ISBN: 978-1-4939-6983-8Published: 05 March 2017

  • eBook ISBN: 978-1-4939-6985-2Published: 01 March 2017

  • Series ISSN: 2191-8198

  • Series E-ISSN: 2191-8201

  • Edition Number: 1

  • Number of Pages: XIII, 124

  • Number of Illustrations: 7 b/w illustrations

  • Topics: Analysis, Solid Mechanics, Classical Mechanics

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