Regularizing effect for unbounded flux-limited viscosity solutions of a discontinuous Hamilton-Jacobi equation on junction

Abstract

In this paper, we provide regularizing effect for continuous bounded from below viscosity solutions of a discontinuous Hamilton-Jacobi equation posed on a junction. We consider different quasi-convex and coercive time-space Hamiltonians on each branch and a flux limiter condition at the junction point. We then prove that the derivative with respect to time of the solution is bounded. As consequence, we deduce that the solution of the equation is locally Lipschitz continuous.