Transport equations and multi-d hyperbolic conservation laws Luigi Ambrosio ... [et al.] ; editors, Fabio Ancona ... [et al.]

Contine bibliogr. si index

Cover -- TOC$Contents -- Part I -- CH$Existence, Uniqueness, Stability and Differentiability Properties of the Flow Associated to Weakly Differentiable Vector Fields -- 1 Introduction -- 2 The Continuity Equation -- 3 The Continuity Equation Within the Cauchy-Lipschitz Framework -- 4 (ODE) Uniqueness Vs. (PDE) Uniqueness -- 5 The Flow Associated to Sobolev or BV Vector Fields -- 6 Measure-Theoretic Differentials -- 7 Differentiability of the Flow in the W1,1 Case -- 8 Differentiability and Compactness of the Flow in the W1,p Case -- 9 Bibliographical Notes and Open Problems -- References -- Part II -- CH$A Note on Alberti's Rank-One Theorem -- 1 Introduction -- 2 Dimensional Reduction -- 3 A Blow-Up Argument Leading to a Partial Result -- 4 The Fundamental Lemma -- 5 Proof of Theorem 1.1 in the Planar Case -- References -- Part III -- CH$Regularizing Effect of Nonlinearity in Multidimensional Scalar Conservation Laws -- 1 Introduction -- 2 Background Material -- 3 Entropy Solutions with BV-Regularity -- 4 Structure of Entropy Solutions -- 5 Kinetic Formulation, Blow-Ups and Split States -- 6 Classification of Split States -- 7 Proof of the Main Theorem -- 8 Proofs of the Regularity Theorems -- References -- IDX$Index -- Last Page