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The theory of nonlinear hyperbolic equations in several space dimensions has recently obtained remarkable achievements. 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. The captivating volume contains surveys of recent deep results and provides an overview of further developments and related open problems. Readers should have basic knowledge of PDE and measure theory.
Preface.- Part I by L. Ambrosio and G. Crippa: Existence, uniqueness, stability and differentiability properties of the flow associated to weakly differentiable vector fields.- Part II by C. De Lellis: A note on Alberti's rank-one theorem.- Part III by G. Crippa, F. Otto and M. Westdickenberg: Regularizing effect of nonlinearity in multidimensional scalar conservation laws.- Index.