Hopf-Lax formula and generalized characteristics

2013/09/10 by Hoang, Nguyen
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1309.2547

Abstract

We study some differential properties of viscosity solution for Hamilton - Jacobi equations defined by Hopf-Lax formula u(t,x)=min_{y∈ \Rⁿ} \σ(y)+tH^* (\frac x-yt) \. 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).

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