Hyperbolic PDEs, Kinetic Formulation, Geometric Measure Theory
Yann Brenier
Université de Nice, France
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Abstract
One of the most fruitful interaction between kinetic theory and non-linear hyperbolic PDEs has been the so-called kinetic formulation of conservation laws. Very recently, within the HYKE network, a beautiful structure theorem for non-smooth solutions of some non-linear hyperbolic PDEs has been obtained by de Lellis, Otto and Westdickenberg [DOW]. The proof is an unusual blend of kinetic ideas, blow-up techniques and tools coming from geometric measure theory.