03421nam a22005535i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001600172072001600188072002300204082001200227100003000239245011300269264004600382300003400428336002600462337002600488338003600514347002400550505027200574520134900846650001702195650002702212650002802239650002502267650002602292650002102318650003602339650002702375650001702402650001402419650002702433650003602460650004702496650002102543700002702564700002802591710003402619773002002653776003602673856004802709912001402757999001902771952007702790978-0-387-68417-8DE-He21320180115171411.0cr nn 008mamaa100301s2009 xxu| s |||| 0|eng d a97803876841789978-0-387-68417-87 a10.1007/978-0-387-68417-82doi 4aQA299.6-433 7aPBK2bicssc 7aMAT0340002bisacsh04a5152231 aAgarwal, Ravi P.eauthor.10aInequalities for Differential Formsh[electronic resource] /cby Ravi P. Agarwal, Shusen Ding, Craig Nolder. 1aNew York, NY :bSpringer New York,c2009. aXVI, 387 p.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aHardy#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. aDuring 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. 0aMathematics. 0aMathematical analysis. 0aAnalysis (Mathematics). 0aIntegral transforms. 0aOperational calculus. 0aOperator theory. 0aPartial differential equations. 0aDifferential geometry.14aMathematics.24aAnalysis.24aDifferential Geometry.24aPartial Differential Equations.24aIntegral Transforms, Operational Calculus.24aOperator Theory.1 aDing, Shusen.eauthor.1 aNolder, Craig.eauthor.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z978038736034840uhttp://dx.doi.org/10.1007/978-0-387-68417-8 aZDB-2-SMA c369559d369559 001040708EBookaelibbelibd2018-01-15r2018-01-15w2018-01-15yEBOOK