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)=y∈ n \σ (y)+tH* ( 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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