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＜E-Book＞
Transport Equations and Multi-D Hyperbolic Conservation Laws / by Luigi Ambrosio, Gianluca Crippa, Camillo De Lellis, Felix Otto, Michael Westdickenberg ; edited by Fabio Ancona, Stefano Bianchini, Rinaldo M. Colombo, Camillo De Lellis, Andrea Marson, Annamaria Montanari
(Lecture Notes of the Unione Matematica Italiana. ISSN:18629121 ; 5)

Edition	1st ed. 2008.
Publisher	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
Year	2008
Language	English
Size	XIV, 131 p : online resource
Authors	*Ambrosio, Luigi author Crippa, Gianluca author De Lellis, Camillo author Otto, Felix author Westdickenberg, Michael author Ancona, Fabio editor Bianchini, Stefano editor Colombo, Rinaldo M editor De Lellis, Camillo editor Marson, Andrea editor Montanari, Annamaria editor SpringerLink (Online service)
Subjects	LCSH:Differential equations LCSH:Mathematical optimization LCSH:Calculus of variations LCSH:Measure theory FREE:Differential Equations FREE:Calculus of Variations and Optimization FREE:Measure and Integration
Notes	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 HTTP:URL=https://doi.org/10.1007/978-3-540-76781-7

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