Preprint 2004-050

Structure of Entropy Solutions for Multi-Dimensional Conservation Laws

Camillo De Lellis, Felix Otto, and Michael Westdickenberg

Abstract: An entropy solution u of a multi-dimensional scalar conservation law is not necessarily in BV, even if the conservation law is genuinely nonlinear. We show that u nevertheless has the structure of a BV-function in the sense that the shock location is codimension-one rectifiable. This result highlights the regularizing effect of genuine nonlinearity in a qualitative way; it is based on the locally finite rate of entropy dissipation. The proof relies on the geometric classification of blow-ups in the framework of the kinetic formulation.

Available as gzipped PostScript (280 Kbytes; uncompress using gunzip).
Camillo De Lellis, <>
Felix Otto
Michael Westdickenberg
Publishing information:
Archive for Rational Mechanics and Analysis 170:137--184
Submitted by:
<> October 12 2004.

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