03117nam 22006735 450 991048429940332120251113204638.09783642183638364218363810.1007/978-3-642-18363-8(CKB)2670000000076214(SSID)ssj0000506047(PQKBManifestationID)11313333(PQKBTitleCode)TC0000506047(PQKBWorkID)10513760(PQKB)10390831(DE-He213)978-3-642-18363-8(MiAaPQ)EBC3066603(PPN)151591377(EXLCZ)99267000000007621420110329d2011 u| 0engurnn#008mamaatxtccrLebesgue and Sobolev Spaces with Variable Exponents /by Lars Diening, Petteri Harjulehto, Peter Hästö, Michael Ruzicka1st ed. 2011.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2011.1 online resource (IX, 509 p. 10 illus.)Lecture Notes in Mathematics,1617-9692 ;2017Bibliographic Level Mode of Issuance: Monograph9783642183621 364218362X Includes bibliographical references and index.1 Introduction -- 2 A framework for function spaces -- 3 Variable exponent Lebesgue spaces -- 4 The maximal operator -- 5 The generalized Muckenhoupt condition* -- 6 Classical operators -- 7 Transfer techniques -- 8 Introduction to Sobolev spaces -- 9. Density of regular functions -- 10. Capacities -- 11 Fine properties of Sobolev functions -- 12 Other spaces of differentiable functions -- 13 Dirichlet energy integral and Laplace equation -- 14 PDEs and fluid dynamics.The field of variable exponent function spaces has witnessed an explosive growth in recent years. The standard reference article for basic properties is already 20 years old. Thus this self-contained monograph collecting all the basic properties of variable exponent Lebesgue and Sobolev spaces is timely and provides a much-needed accessible reference work utilizing consistent notation and terminology. Many results are also provided with new and improved proofs. The book also presents a number of applications to PDE and fluid dynamics.Lecture Notes in Mathematics,1617-9692 ;2017Mathematical analysisFunctional analysisDifferential equationsAnalysisFunctional AnalysisDifferential EquationsMathematical analysis.Functional analysis.Differential equations.Analysis.Functional Analysis.Differential Equations.515Diening Lars478953MiAaPQMiAaPQMiAaPQBOOK9910484299403321Lebesgue and sobolev spaces with variable exponents261811UNINA