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A note on admissible solutions of 1D scalar conservation laws and 2D Hamilton-Jacobi equations


Ambrosio, L; De Lellis, C (2004). A note on admissible solutions of 1D scalar conservation laws and 2D Hamilton-Jacobi equations. Journal of Hyperbolic Differential Equations, 1(4):813-826.

Abstract

Let Ω⊂ℝ2 be an open set and 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.

Let Ω⊂ℝ2 be an open set and 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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Hopf–Lax formula; BV functions; SBV functions; entropy solutions
Language:English
Date:2004
Deposited On:17 Sep 2010 07:19
Last Modified:05 Apr 2016 13:24
Publisher:World Scientific Publishing
ISSN:0219-8916
Additional Information:Preprint of an article submitted for consideration in [J. Hyperbolic Differ. Equ.] © 2004 copyright World Scientific Publishing Company http://www.worldscinet.com/jhde/jhde.shtml
Publisher DOI:https://doi.org/10.1142/S0219891604000263
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2111584
Permanent URL: https://doi.org/10.5167/uzh-21763

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