Overview
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 in the subject
Invaluable as a reference work for researchers in fields such as general relativity, theory of elasticity, quasiconformal analysis, differential geometry, and nonlinear differential equations in domains and on manifolds
Includes supplementary material: sn.pub/extras
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Table of contents (9 chapters)
Keywords
About this book
Differential 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 such differential forms in particular. It concentrates on the Hardy-Littlewood, Poincaré, Cacciooli, imbedded and reverse Holder inequalities. Integral estimates for operators, such as homotopy operator, the Laplace-Beltrami operator, and the gradient operator are also presented. 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 book 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.
Authors and Affiliations
Bibliographic Information
Book Title: Inequalities for Differential Forms
Authors: Ravi P. Agarwal, Shusen Ding, Craig Nolder
DOI: https://doi.org/10.1007/978-0-387-68417-8
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag New York 2009
Hardcover ISBN: 978-0-387-36034-8Published: 05 October 2009
Softcover ISBN: 978-1-4899-8351-0Published: 05 September 2014
eBook ISBN: 978-0-387-68417-8Published: 19 September 2009
Edition Number: 1
Number of Pages: XVI, 388
Topics: Analysis, Differential Geometry, Partial Differential Equations, Integral Transforms, Operational Calculus, Operator Theory