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 presenta series of local and global estimates and inequalities for such differentialforms 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 gradientoperator are also presented. Additionally, some related topics such as BMO inequalities, Lipschitz classes, Orlicz spaces and inequalities in Carnot groupsare 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. INDICE: Hardy-Littlewood Inequalities.- Norm Comparison Theorems.- Poincaré-type inequalities.- Caccioppoli Inequalities.- Imbedding Theorems.- Reverse Holder Inequalities.- Inequalities for Operators.- Estimates for Jacobians.- Lipschitz and BMO norms.- References.- Index.
- ISBN: 978-0-387-36034-8
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 370
- Fecha Publicación: 01/10/2009
- Nº Volúmenes: 1
- Idioma: Inglés