Metric formulae for nonconvex Hamilton--Jacobi equations and applications
Metric formulae for nonconvex Hamilton--Jacobi equations and applications
We consider the Hamilton-Jacobi equation $H(x,Du)=0$ in $\mathbb R^n$, with $H$ not enjoying any convexity properties in the second variable. Our aim is to establish existence and nonexistence theorems for viscosity solutions of associated Dirichlet problems, find representation formulae and prove comparison principles. Our analysis is based on the introduction …