Transport equations and multi-D hyperbolic conservation laws

Luigi Ambrosio, Gianluca Crippa, Felix Otto, Michael Westdickenberg, Camillo De Lellis, Camillo De Lellis, Fabio Ancona, Stefano Bianchini, Rinaldo M. Colombo, Andrea Marson, Annamaria Montanari3540767800, 9783540767800

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.

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Table of contents :
Cover……Page 1
Lecture Notes of the Unione Matematica Italiana 5……Page 2
Transport Equations and Multi-D Hyperbolic Conservation Laws……Page 4
Preface……Page 6
Contents……Page 11
Authors……Page 13
Editors……Page 14
Existence, Uniqueness, Stability and Differentiability Properties of the Flow Associated to Weakly Differentiable Vector Fields……Page 15
A Note on Alberti’s Rank-One Theorem……Page 70
Regularizing Effect of Nonlinearity in Multidimensional Scalar Conservation Laws……Page 84
Index……Page 136