Semi-concave Singularities and the Hamilton–Jacobi Equation

    2013, Volume 18, Number 6, pp.  674-685

    Author(s): Bernard P.

    We study the Cauchy problem for the Hamilton–Jacobi equation with a semiconcave initial condition.We prove an inequality between two types of weak solutions emanating from such an initial condition (the variational and the viscosity solution).We also give conditions for an explicit semi-concave function to be a viscosity solution. These conditions generalize the entropy inequality characterizing piecewise smooth solutions of scalar conservation laws in dimension one.
    Keywords: Hamilton–Jacobi equations, viscosity solutions, variational solutions, calculus of variations
    Citation: Bernard P., Semi-concave Singularities and the Hamilton–Jacobi Equation, Regular and Chaotic Dynamics, 2013, Volume 18, Number 6, pp. 674-685

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