Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.
MiS Preprint
95/2002
Structure of entropy solutions for multi--dimensional scalar 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.
