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Inequalities for Differential Forms

  • Ravi P. Agarwal
  • Shusen Ding
  • Craig Nolder

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Ravi P. Agarwal, Shusen Ding, Craig Nolder
    Pages 1-56
  3. Ravi P. Agarwal, Shusen Ding, Craig Nolder
    Pages 57-73
  4. Ravi P. Agarwal, Shusen Ding, Craig Nolder
    Pages 75-117
  5. Ravi P. Agarwal, Shusen Ding, Craig Nolder
    Pages 119-143
  6. Ravi P. Agarwal, Shusen Ding, Craig Nolder
    Pages 145-185
  7. Ravi P. Agarwal, Shusen Ding, Craig Nolder
    Pages 187-223
  8. Ravi P. Agarwal, Shusen Ding, Craig Nolder
    Pages 225-321
  9. Ravi P. Agarwal, Shusen Ding, Craig Nolder
    Pages 323-337
  10. Ravi P. Agarwal, Shusen Ding, Craig Nolder
    Pages 339-367
  11. Back Matter
    Pages 1-18

About this book

Introduction

During the recent years, differential forms have played an important role in many fields. In particular, the forms satisfying the A-harmonic equations, have found wide applications in fields such as general relativity, theory of elasticity, quasiconformal analysis, differential geometry, and nonlinear differential equations in domains on manifolds.

This monograph is the first one to systematically present a series of local and global estimates and inequalities for differential forms.  The presentation concentrates on the Hardy-Littlewood, Poincare, Cacciooli, imbedded and reverse Holder inequalities.  Integral estimates for operators, such as homotopy operator, the Laplace-Beltrami operator, and the gradient operator are also covered.  Additionally, some related topics such as BMO inequalities, Lipschitz classes, Orlicz spaces and inequalities in Carnot groups are discussed in the concluding chapter.  An abundance of bibliographical references and historical material supplement the text throughout.

This rigorous text requires a familiarity with topics such as differential forms, topology and Sobolev space theory.  It will serve as an invaluable reference for researchers, instructors and graduate students in analysis and partial differential equations and could be used as additional material for specific courses in these fields.

Keywords

Differential Equations Sobolev space a-harmonic equations differential geometry general relativity manifold partial differential equation quasiconformal analysis theory of elasticity

Authors and affiliations

  • Ravi P. Agarwal
    • 1
  • Shusen Ding
    • 2
  • Craig Nolder
    • 3
  1. 1.Dept. Mathematical SciencesFlorida Institute of TechnologyMelbourneU.S.A.
  2. 2.Mathematics Dept.Seattle UniversitySeattleU.S.A.
  3. 3.Dept. MathematicsFlorida State UniversityTallahasseeU.S.A.

Bibliographic information