# Metric Viscosity Solutions of Hamilton-Jacobi Equations Depending on Local Slopes.

## Wilfrid Gangbo

### (Georgia Tech.)

Date: Oct 29, 2014, time: 09:55

Abstract. We present a theory of metric viscosity solutions which encompasses a large class of Hamiltonians. We consider time dependent problems
$\label{a111} \partial_tu+H(t,x,u,\vert\nabla u\vert)=0,\quad\mbox{in}\,\,(0,T)\times \Omega,$
\label{a111BC}
\left\{
\begin{array}{ll}
&