Hopf-type estimates for solutions to Hamilton-Jacobi equations with concave-convex initial data

Abstract

We consider the Cauchy problem for the Hamilton-Jacobi equations with concave-convex initial data. A Hopf-type formula for global Lipschitz solutions and estimates for viscosity solutions of this problem are obtained using techniques of multifunctions and convex analysis.

Keywords

• Hamilton-Jacobi equations
• Hopf-type formula
• global Lipschitz solutions
• viscosity solutions