Inequalities for Differential Forms [electronic resource] / by Ravi P. Agarwal, Shusen Ding, Craig Nolder.

By: Agarwal, Ravi P [author.]
Contributor(s): Ding, Shusen [author.] | Nolder, Craig [author.] | SpringerLink (Online service)
Material type: TextTextPublisher: New York, NY : Springer New York, 2009Description: XVI, 387 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9780387684178Subject(s): Mathematics | Mathematical analysis | Analysis (Mathematics) | Integral transforms | Operational calculus | Operator theory | Partial differential equations | Differential geometry | Mathematics | Analysis | Differential Geometry | Partial Differential Equations | Integral Transforms, Operational Calculus | Operator TheoryAdditional physical formats: Printed edition:: No titleDDC classification: 515 LOC classification: QA299.6-433Online resources: Click here to access online
Contents:
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.
In: Springer eBooksSummary: 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.
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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.

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.

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