Some regularity properties of viscosity solution defined by Hopf formula

2016/04/14 by Hoang, Nguyen
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1604.04060

Abstract

Some properties of characteristic curves in connection with viscosity solution of Hamilton-Jacobi equations (H,σ) defined by Hopf formula u(t,x)=max_q∈\Rⁿ\ ⟨ x,q⟩ -σ^*(q)-tH(q)\ are studied. We are concerned with the points where the solution u(t,x) is differentiable, and the strip of the form \mathcal R=(0,t₀)× \Rⁿ of the domain Ω where u(t,x) is of class C¹(\mathcal R). Moreover, we investigate the propagation of singularities in forward of this solution.

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