Title A note on admissible solutions of 1D scalar conservation laws and 2D Hamilton-Jacobi equations. Publication Type Journal Article Year of Publication 2004 Authors Ambrosio L., De Lellis C. Journal Journal of Hyperbolic Differential Equations Volume 1 Pagination 813–826 Publisher World Scientific Publishing Type of Article scalar ISSN 0219-8916 Keywords BV functions, entropy solutions, Hopf?Lax formula, SBV functions Abstract Let ??$R$2 be an open set and f?C2($R$) with f" \ensuremath> 0. In this note we prove that entropy solutions of Dtu+Dxf(u) = 0 belong to SBVloc(?). As a corollary we prove the same property for gradients of viscosity solutions of planar Hamilton?Jacobi PDEs with uniformly convex Hamiltonians. Notes J. Hyperbolic Differ. Equ. 1 (2004), no. 4, 813–826. URL http://www.worldscinet.com/jhde/01/0104/S0219891604000263.html DOI 10.1142/S0219891604000263
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