Author	Ambrosio, Luigi. author
Title	Transport Equations and Multi-D Hyperbolic Conservation Laws [electronic resource] / by Luigi Ambrosio, Gianluca Crippa, Camillo Lellis, Felix Otto, Michael Westdickenberg
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg, 2008
Connect to	http://dx.doi.org/10.1007/978-3-540-76781-7
Descript	XIV, 131 p. online resource

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

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

1. Mathematics
2. Differential Equations
3. Differential equations
4. partial
5. Mathematical optimization
6. Mathematics
7. Partial Differential Equations
8. Ordinary Differential Equations
9. Calculus of Variations and Optimal Control; Optimization
10. Measure and Integration