A maximum principle for evolution Hamilton-Jacobi equations on Riemannian manifolds

Abstract

We establish a maximum principle for viscosity subsolutions and supersolutions of equations of the form u(t) + F(t, d(x)u) = 0, u(0, x) = u(0)(x), where u(0): M -> R is a bounded uniformly continuous function, M is a Riemannian manifold, and F: [0, infinity) x T*M -> R. This yields uniqueness of the viscosity solutions of such Hamilton-Jacobi equations.