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Inequalities for Differential Forms / by Ravi P. Agarwal, Shusen Ding, Craig Nolder
Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: SpringerLink BücherPublisher: New York, NY : Springer-Verlag New York, 2009Description: Online-Ressource (digital)ISBN:- 9780387684178
- 1282363069
- 9780387360348
- 9781282363069
- Differentialgeometrie
- Differentialform
- Ungleichung
- Differential geometry
- Partial differential equations
- Mathematical analysis
- Operational calculus
- Analysis (Mathematics)
- Differential equations, partial
- Global analysis (Mathematics)
- Global differential geometry
- Integral Transforms
- Mathematics
- Operator theory
- 516.36
- 515 23
- 515.35 515.36
- QA641-670
- QA381
Contents:
Summary: 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.Summary: 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.PPN: PPN: 1648443559Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SXMS | ZDB-2-SMA
Preface; Contents; Hardy--Littlewood inequalities; Norm comparison theorems; Poincaré-type inequalities; Caccioppoli inequalities; Imbedding theorems; Reverse Hölder inequalities; Inequalities for operators; Estimates for Jacobians; Lipschitz and BMO norms; References; Index;
CoverPreface -- Contents -- Hardy -- Littlewood inequalities -- Differential forms -- Basic elements -- Definitions and notations -- Poincar233; lemma -- A-harmonic equations -- Quasiconformal mappings -- A-harmonic equations -- p-Harmonic equations -- Two equivalent forms -- Three-dimensional cases -- The equivalent system -- An example -- Some weight classes -- Ar()-weights -- Ar(, E)-weights -- Ar (E)-weights -- Some classes of two-weights -- Inequalities in John domains -- Local inequalities -- Weighted inequalities -- Global inequalities -- Inequalities in averaging domains -- Averaging domains -- Ls()-averaging domains -- Other weighted inequalities -- Two-weight cases -- Local inequalities -- Global inequalities -- The best integrable condition -- An example -- Remark -- Inequalities with Orlicz norms -- Norm comparison theorem -- Lp (logL)-norm inequality -- Ar()-weighted case -- Global Ls(logL)-norm inequality -- Norm comparison theorems -- Introduction -- The local unweighted estimates -- Basic Lp-inequalities -- Special cases -- The local weighted estimates -- Ls-estimates for dv -- Ls-estimates for du -- The norm comparison between d and d -- The global estimates -- Global estimates for dv -- Global estimates for du -- Global Lp-estimates -- Global Ls-estimates -- Applications -- Imbedding theorems for differential forms -- Poincar233;-type inequalities -- Introduction -- Inequalities for differential forms -- Basic inequalities -- Weighted inequalities -- Inequalities for harmonic forms -- Global inequalities in averaging domains -- Ar-weighted inequalities -- Inequalities for Green's operator -- Basic estimates for operators -- Weighted inequality for Green's operator -- Global inequality for Green's operator -- Inequalities with Orlicz norms -- Local inequality -- Weighted inequalities -- The proof of the global inequality -- Two-weight inequalities -- Statements of two-weight inequalities -- Proofs of the main theorems -- Ar()-weighted inequalities -- Inequalities for Jacobians -- Some notations -- Two-weight estimates -- Inequalities for the projection operator -- Statement of the main theorem -- Inequality for and G -- Proof of the main theorem -- Other Poincar233;-type inequalities -- Caccioppoli inequalities -- Preliminary results -- Local and global weighted cases -- Ar()-weighted inequality -- Ar(,)-weighted inequality -- Ar()-weighted inequality -- Parametric version -- Inequalities with two parameters -- Local and global two-weight cases -- An unweighted inequality -- Two-weight inequalities -- Inequalities with Orlicz norms -- Basic "026B30D "026B30D Lp(logL)(E) estimates -- Weak reverse H246;lder inequalities -- Ar(M)-weighted cases -- Inequalities with the codifferential operator -- Lq-estimate for dv -- Two-weight estimate for dv -- Imbedding theorems -- Introduction -- Quasiconformal mappings -- Solutions to the nonhomogeneous equation -- Imbedding inequalities for operators -- The gradient and homotopy operators -- Some special cases -- Global imbedding theorems -- Other weighted cases -- Ls.
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