Divergence Operator and Related Inequalities

  • Gabriel Acosta
  • Ricardo G. Durán

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Gabriel Acosta, Ricardo G. Durán
    Pages 1-12
  3. Gabriel Acosta, Ricardo G. Durán
    Pages 13-45
  4. Gabriel Acosta, Ricardo G. Durán
    Pages 47-60
  5. Gabriel Acosta, Ricardo G. Durán
    Pages 61-97
  6. Back Matter
    Pages 99-124

About this book

Introduction

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.

Keywords

Korn's Inequalities Right Inverse of the Divergence Operator Improved Poincare Inequalities Weighted Sobolev Spaces John Domains Singular Domains

Authors and affiliations

  • Gabriel Acosta
    • 1
  • Ricardo G. Durán
    • 2
  1. 1.Department of Mathematics and IMASUniversity of Buenos Aires and CONICETBuenos AiresArgentina
  2. 2.Department of Mathematics and IMASUniversity of Buenos Aires and CONICETBuenos AiresArgentina

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4939-6985-2
  • Copyright Information The Author(s) 2017
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4939-6983-8
  • Online ISBN 978-1-4939-6985-2
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • About this book
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