Hopf-Lax formula and generalized characteristics

Abstract

We study some differential properties of viscosity solution for Hamilton - Jacobi equations defined by Hopf-Lax formula $u(t,x)={\min }_{y\in {\mathbb{R}}^n}\{\sigma (y)+t{H}^{\ast }(\frac{x-y}{t}\left)\right\}.$ A generalized form of characteristics of the Cauchy problems is taken into account the context. Then we examine the strip of differentiability of the viscosity solution given by the function $u(t,x).$

arXiv comment15 pages. arXiv admin note: text overlap with arXiv:1208.3288