Inequalities for Differential Forms

2010
ISBN: 978-0-387-36034-8
Verlag: Springer

Buch, Englisch, 388 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1640 g

This monograph is the first one to systematically present a series of local and global estimates and inequalities for differential forms, in particular the ones that satisfy the A-harmonic equations. The presentation focuses 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 discussed next.  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 presentation 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.

Zielgruppe

Research

Autoren/Hrsg.

Agarwal, Ravi P.

Nolder, Craig

Ding, Shusen

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie

Inhaltsverzeichnis

Hardy#x2013;Littlewood inequalities.- Norm comparison theorems.- Poincar#x00E9;-type inequalities.- Caccioppoli inequalities.- Imbedding theorems.- Reverse H#x00F6;lder inequalities.- Inequalities for operators.- Estimates for Jacobians.- Lipschitz and norms.