Book Cover
E-book
Author Agarwal, Ravi P.

Title Inequalities for differential forms / Ravi P. Agarwal, Shusen Ding and Craig Nolder
Published New York : Springer, [2009]
©2009
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Description 1 online resource (xvi, 387 pages)
Contents Cover -- Preface -- 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
Summary Presents a series of local and global estimates and inequalities for differential forms, in particular the ones that satisfy the A-harmonic equations. This work focuses on the Hardy-Littlewood, Poincare, Cacciooli, imbedded and reverse Holder inequalities. It is for researchers, instructors and graduate students
Bibliography Includes bibliographical references and index
Notes Print version record
Subject Differential inequalities.
Differential forms.
Form Electronic book
Author Ding, Shushen.
Nolder, Craig.
LC no. 2009931765
ISBN 0387360344 (Cloth)
0387684174
9780387360348 (Cloth)
9780387684178