Inserted: 14 nov 2002
Last Updated: 3 may 2011
Journal: Archive for Rational Mechanics and Analysis
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.
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Keywords: Partial regularity, Rectifiability, conservation laws, entropy solutions, shocks