Numerical viscosity solutions to Hamilton-Jacobi equations via a Carleman estimate and the convexification method

Viscosity Solutions of Hamilton-Jacobi Equations

Problems involving Hamilton-Jacobi equations-which we take to be either of the stationary form H(x, u, Du) = 0 or of the evolution form u, + H(x, t, u, Du) = 0, where Du is the spatial gradient of u-arise in many contexts. Classical analysis of associated problems under boundary and/or initial conditions by the method of characteristics is limited to local considerations owing to the crossing o...

On Viscosity Solutions of Hamilton-jacobi Equations

We consider the Dirichlet problem for Hamilton-Jacobi equations and prove existence, uniqueness and continuous dependence on boundary data of Lipschitz continuous maximal viscosity solutions.

Metric Viscosity Solutions of Hamilton-jacobi Equations

A theory of viscosity solutions in metric spaces based on local slopes was initiated in [39]. In this manuscript we deepen the study of [39] and present a more complete account of the theory of metric viscosity solutions of Hamilton–Jacobi equations. Several comparison and existence results are proved and the main techniques for such metric viscosity solutions are illustrated.

Viscosity solutions of discontinuous Hamilton–Jacobi equations

We define viscosity solutions for the Hamilton–Jacobi equation φt = v(x, t)H(∇φ) in RN × (0,∞) where v is positive and bounded measurable and H is non-negative and Lipschitz continuous. Under certain assumptions, we establish the existence and uniqueness of Lipschitz continuous viscosity solutions. The uniqueness result holds in particular for those v which are independent of t and piecewise co...

Viscosity Solutions of Hamilton-Jacobi Equations and Optimal Control Problems