Transport Equations and Multi-D Hyperbolic Conservation Laws

• Main Authors: Ambrosio, Luigi (Author), Crippa, Gianluca (Author), Lellis, Camillo De (Author), Otto, Felix (Author), Westdickenberg, Michael (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2008.
• Series: Lecture Notes of the Unione Matematica Italiana, 5
• Subjects: Mathematics.; Measure theory.; Differential equations.; Partial differential equations.; Calculus of variations.; Partial Differential Equations.; Ordinary Differential Equations.; Calculus of Variations and Optimal Control; Optimization.; Measure and Integration.

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 perspect...

Table of Contents:

• 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.