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.
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.
| 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: | 23 Jan 2022 14:35 |
| 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 |
| OA Status: | Green |
| Publisher DOI: | https://doi.org/10.1142/S0219891604000263 |
| Related URLs: | http://www.ams.org/mathscinet-getitem?mr=2111584 |
Ambrosio, L