Inequalities for Differential Forms by Ravi P. Agarwal & Shusen Ding
English | 2009 | ISBN: 0387360344, 1489983511 | 370 pages | PDF | 1,9 MB
This monograph is the first one to systematically present a series of local & global estimates & inequalities for differential forms, in particular the ones that satisfy the A-harmonic equations. The presentation focuses on the Hardy-Littlewood, Poincare, Cacciooli, imbedded & reverse Holder inequalities. Integral estimates for operators, such as homotopy operator, the Laplace-Beltrami operator, & the gradient operator are discussed next. Additionally, some related topics such as BMO inequalities, Lipschitz classes, Orlicz spaces & inequalities in Carnot groups are discussed in the concluding chapter. An abundance of bibliographical references & historical material supplement the text throughout.
This rigorous presentation requires a familiarity with topics such as differential forms, topology & Sobolev space theory. It will serve as an invaluable reference for researchers, instructors & graduate students in analysis & partial differential equations & could be used as additional material for specific courses in these fields.