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A NOTE ON ADMISSIBLE SOLUTIONS OF 1D SCALAR CONSERVATION LAWS AND 2D HAMILTON–JACOBI EQUATIONS

    https://doi.org/10.1142/S0219891604000263Cited by:27 (Source: Crossref)

    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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