Preprint 2004-057

A Note on Admissible Solutions of 1D Scalar Conservation Laws and 2D Hamilton-Jacobi Equations

Luigi Ambrosio and Camillo De Lellis

Abstract: Let Ω⊂ℜ2 be an open set and let f∈C2(ℜ) with f''>0. In this note we prove that entropy solutions of Dtu + Dxf(u)=0 belong to SBVloc(Ω). As a corollary we prove the same property for gradients of viscosity solutions of planar Hamilton--Jacobi PDEs with uniformly convex hamiltonians.


Paper:
Available as gzipped PostScript (120 Kbytes; uncompress using gunzip).
Author(s):
Luigi Ambrosio <l.ambrosio@sns.it>
Camillo De Lellis, <delellis@math.unizh.ch>
Publishing information:
To appear in Journal of Hyperbolic Differential Equations
Comments:
Submitted by:
<delellis@math.unizh.ch> October 12 2004.


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