03425nam 2200661Ia 450 991045171800332120200520144314.01-281-23169-X97866112316993-540-76781-910.1007/978-3-540-76781-7(CKB)1000000000492129(EBL)336743(OCoLC)233973697(SSID)ssj0000311937(PQKBManifestationID)11230272(PQKBTitleCode)TC0000311937(PQKBWorkID)10330767(PQKB)10445447(DE-He213)978-3-540-76781-7(MiAaPQ)EBC336743(PPN)123743028(Au-PeEL)EBL336743(CaPaEBR)ebr10223697(CaONFJC)MIL123169(EXLCZ)99100000000049212920070322d2008 uy 0engur|n|---|||||txtccrTransport equations and multi-D hyperbolic conservation laws[electronic resource] /Luigi Ambrosio ... [et al.] ; editors, Fabio Ancona ... [et al.]1st ed. 2008.Berlin ;New York Springerc20081 online resource (142 p.)Lecture notes of the Unione Matematica Italiana,1862-9113 ;5Description based upon print version of record.3-540-76780-0 Includes bibliographical references and index.I -- Existence, Uniqueness, Stability and Differentiability Properties of the Flow Associated to Weakly Differentiable Vector Fields -- II -- A Note on Alberti's Rank-One Theorem -- III -- Regularizing Effect of Nonlinearity in Multidimensional Scalar Conservation Laws.The theory of nonlinear hyperbolic equations in several space dimensions has recently obtained remarkable achievements thanks to ideas and techniques related to the structure and fine properties of functions of bounded variation. This volume provides an up-to-date overview of the status and perspectives of two areas of research in PDEs, related to hyperbolic conservation laws. Geometric and measure theoretic tools play a key role to obtain some fundamental advances: the well-posedness theory of linear transport equations with irregular coefficients, and the study of the BV-like structure of bounded entropy solutions to multi-dimensional scalar conservation laws. The volume contains surveys of recent deep results, provides an overview of further developments and related open problems, and will capture the interest of members both of the hyperbolic and the elliptic community willing to explore the intriguing interplays that link their worlds. Readers should have basic knowledge of PDE and measure theory.Lecture notes of the Unione Matematica Italiana ;5.Conservation laws (Mathematics)Differential equations, HyperbolicElectronic books.Conservation laws (Mathematics)Differential equations, Hyperbolic.515/.782Ambrosio Luigi44009Ancona Fabio1964-738757MiAaPQMiAaPQMiAaPQBOOK9910451718003321Transport equations and multi-D hyperbolic conservation laws1958022UNINA