Hopf-Lax type formula for non monotonic autonomous Hamilton Jacobi equations

Abstract.

We give an explicit formula for a solution of Hamilton-Jacobi equation u _t +H(u,Du)=0 in $\mathbb{R}^n \times \mathbb{R}_ +$ with initial condition u(x,0)=u₀(x), where p→ H(u,p) is convex, positively homogeneous of degree one and the Hamiltonian H need not satisfy the monotonicity condition in u.