Inequalities for Differential Forms

Authors: Agarwal, Ravi P., Ding, Shusen, Nolder, Craig

  • Bridges the gap in literature and research on inequalities and estimates for differential forms satisfying A-harmonic equations
  • Provides extensions of one dimensional results in real space and the application of these results in different geometric structures on differentiable manifolds
  • Well-written documentation of up-to-date advances on the subject
  • Invaluable as a reference work for researchers in general relativity, theory of elasticity, quasiconformal analysis, differential geometry, and nonlinear differential equations in domains and on manifolds
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eBook $129.00
price for USA (gross)
  • ISBN 978-0-387-68417-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.00
price for USA
  • ISBN 978-0-387-36034-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $169.00
price for USA
  • ISBN 978-1-4899-8351-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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.

Table of contents (9 chapters)

  • Hardy–Littlewood inequalities

    Agarwal, Ravi P. (et al.)

    Pages 1-56

  • Norm comparison theorems

    Agarwal, Ravi P. (et al.)

    Pages 57-73

  • Poincaré-type inequalities

    Agarwal, Ravi P. (et al.)

    Pages 75-117

  • Caccioppoli inequalities

    Agarwal, Ravi P. (et al.)

    Pages 119-143

  • Imbedding theorems

    Agarwal, Ravi P. (et al.)

    Pages 145-185

Buy this book

eBook $129.00
price for USA (gross)
  • ISBN 978-0-387-68417-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.00
price for USA
  • ISBN 978-0-387-36034-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $169.00
price for USA
  • ISBN 978-1-4899-8351-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Inequalities for Differential Forms
Authors
Copyright
2009
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-0-387-68417-8
DOI
10.1007/978-0-387-68417-8
Hardcover ISBN
978-0-387-36034-8
Softcover ISBN
978-1-4899-8351-0
Edition Number
1
Number of Pages
XVI, 387
Topics