Geometric conditions for regularity of viscosity solution to the simplest Hamilton-Jacobi equation

Abstract

Continuing research <cite>GP1, GP2</cite> on the well-posedness of the time-minimum problem with a constant convex dynamics (in a Hilbert space), we adapt one of the regularity conditions obtained there to a slightly more general problem, where nonaffine additive term appears. We prove existence and uniqueness of a minimizer in this problem as well as continuous differentiability of the value function (it can be seen as the viscosity solution to a Hamilton-Jacobi equation) near the boundary of the domain