Inequalities for Differential Forms - Hardcover

Agarwal, Ravi P.; Ding, Shusen; Nolder, Craig

Hardcover

ISBN 10: 0387360344 ISBN 13: 9780387360348

Verlag: Springer, 2009

Inhaltsangabe

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.

Über diesen Titel

Über die Autorin bzw. den Autor

Ravi P. Agarwal is a Professor at the Texas A&M University in Kingsville, USA. He is also a Distinguished University Professor of Mathematics at the Florida Institute of Technology, Melbourne, FL, USA. He did his PhD at the Indian Institute of Technology, India. Dr. Agarwal authored, co-authored and co-edited over 60 books, including "An Introduction to Ordinary Differential Equations" (978-0-387-71275-8) and "Ordinary and Partial Differential Equations" (978-0-387-79145-6), both co-authored by Donal O'Regan and published by Springer.

Simona Hodis is an Assistant Professor at the Texas A&M University in Kingsville, USA. She got her PhD from the University of Western Ontario, Canada. Her research interests include mathematical modeling in medicine and engineering, fluid dynamics, applied mathematics, partial differential equations, and numerical analysis.

Donal O'Regan is a Professor at the National University of Ireland.His research interests are in nonlinear functional analysis. His previous publications with Springer include "Constant-Sign Solutions of Systems of Integral Equations" (978-3-319-01254-4) and "Fixed Point Theory for Lipschitzian-type Mappings with Applications" (978-0-387-75817-6), both as a co-author.

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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.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2009
• Sprache: Englisch
• ISBN 10: 0387360344
• ISBN 13: 9780387360348
• Einband: Gebundene Ausgabe
• Anzahl der Seiten: 404
• Kontakt zum Hersteller: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Deutschland