Hopf-Lax formula and generalized characteristics

Abstract

We study some differential properties of viscosity solutions for Hamilton–Jacobi equations defined by Hopf-Lax formula A generalized form of characteristics of the Cauchy problem is taken into account the context. Then we examine the strip of differentiability of the viscosity solution given by the function u(t, x).

Keywords:

• Hamilton–Jacobi equation
• Hopf-Lax formula
• generalized characteristics
• viscosity solution
• semiconvexity
• semiconcavity

AMS Subject Classifications:

• 35D40
• 35F21
• 35E10
• 52A41

Notes

No potential conflict of interest was reported by the author.

Additional information

Funding

This research is partially supported by the NAFOSTED, Vietnam [grant number 101.02-2013.09] and by the project [DHH2013-03-35].