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Table of contents

  1. Front Matter
    Pages i-xv
  2. Alexander A. Balinsky, W. Desmond Evans, Roger T. Lewis
    Pages 1-48
  3. Alexander A. Balinsky, W. Desmond Evans, Roger T. Lewis
    Pages 49-76
  4. Alexander A. Balinsky, W. Desmond Evans, Roger T. Lewis
    Pages 77-134
  5. Alexander A. Balinsky, W. Desmond Evans, Roger T. Lewis
    Pages 135-164
  6. Alexander A. Balinsky, W. Desmond Evans, Roger T. Lewis
    Pages 165-212
  7. Alexander A. Balinsky, W. Desmond Evans, Roger T. Lewis
    Pages 213-249
  8. Back Matter
    Pages 251-263

About this book

Introduction

This volume presents advances that have been made over recent decades in areas of research featuring Hardy's inequality and related topics. The inequality and its extensions and refinements are not only of intrinsic interest but are indispensable tools in many areas of mathematics and mathematical physics.

Hardy inequalities on domains have a substantial role and this necessitates a detailed investigation of significant geometric properties of a domain and its boundary. Other topics covered in this volume are Hardy- Sobolev-Maz’ya inequalities; inequalities of Hardy-type involving magnetic fields; Hardy, Sobolev and Cwikel-Lieb-Rosenbljum inequalities for Pauli operators; the Rellich inequality.
 
The Analysis and Geometry of Hardy’s Inequality provides an up-to-date account of research in areas of contemporary interest and would be suitable for a graduate course in mathematics or physics. A good basic knowledge of real and complex analysis is a prerequisite.

Keywords

Boundary Curvatures Hardy Inequalities on Domains Magnetic Fields Mean Curvature Mean Distance Function Non-Convex Domains Pauli Operator Rellich Inequality Ridge and Skeleton of Domains

Authors and affiliations

  • Alexander A. Balinsky
    • 1
  • W. Desmond Evans
    • 2
  • Roger T. Lewis
    • 3
  1. 1.School of MathematicsCardiff UniversityCardiffUnited Kingdom
  2. 2.School of MathematicsCardiff UniversityCardiffUnited Kingdom
  3. 3.Department of MathematicsUniversity of Alabama at BirminghamBirminghamUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-22870-9
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-22869-3
  • Online ISBN 978-3-319-22870-9
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site
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