03386nam 22006375 450 991025430890332120250113172301.010.1007/978-1-4939-6985-2(CKB)3710000001084294(DE-He213)978-1-4939-6985-2(MiAaPQ)EBC4816268(PPN)199764476(EXLCZ)99371000000108429420170302d2017 u| 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrierDivergence operator and related inequalities /by Gabriel Acosta, Ricardo G. Durán1st ed. 2017.New York, NY :Springer New York :Imprint: Springer,2017.1 online resource (XIII, 124 p. 7 illus.)SpringerBriefs in Mathematics,2191-81989781493969852 1493969854 9781493969838 1493969838 Includes bibliographical references and index.Introduction -- Divergence Operator -- Korn's Inequalities -- Singular Domains -- Basic Equations of Continuum Mechanics -- Powers of the Distance to the Boundary as Ap Weights -- An Auxiliary Result on Holder a Domains.This Brief is mainly devoted to two classical and related results: the existence of a right inverse of the divergence operator and the so-called Korn Inequalities. It is well known that both results are fundamental tools in the analysis of some classic differential equations, particularly in those arising in fluid dynamics and elasticity. Several connections between these two topics and improved Poincaré inequalities are extensively treated. From simple key ideas the book is growing smoothly in complexity. Beginning with the study of these problems on star-shaped domains the arguments are extended first to John domains and then to Hölder α domains where the need of weighted spaces arises naturally. In this fashion, the authors succeed in presenting in an unified and concise way several classic and recent developments in the field. These features certainly makes this Brief useful for students, post-graduate students, and researchers as well.SpringerBriefs in Mathematics,2191-8198Mathematical analysisMathematical analysisMechanicsMechanics, AppliedAnalysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12007Solid Mechanicshttps://scigraph.springernature.com/ontologies/product-market-codes/T15010Classical Mechanicshttps://scigraph.springernature.com/ontologies/product-market-codes/P21018Mathematical analysis.Mathematical analysis.Mechanics.Mechanics, Applied.Analysis.Solid Mechanics.Classical Mechanics.515.26Acosta Gabrielauthttp://id.loc.gov/vocabulary/relators/aut767351Durán Ricardo Gauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910254308903321Divergence Operator and Related Inequalities2238304UNINA