Some Regularity Properties of Viscosity Solution Defined by Hopf Formula
نویسنده
چکیده
Some properties of characteristic curves in connection with viscosity solution of Hamilton-Jacobi equations (H,σ) defined by Hopf formula u(t, x) = maxq∈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 formR = (0, t0)×R of the domain Ω where u(t, x) is of class C1(R). Moreover, we investigate the propagation of singularities in forward of this solution.
منابع مشابه
Topics on optimal control and PDEs
The course deals with the analysis of optimal control problems and of the related first order PDEs of dynamic programming. In particular, we shall focus our attention on time optimal control problems for linear and nonlinear systems. We shall present some recent results concerning the regularity and the compactness of viscosity solutions to Hamilton-Jacobi and Hamilton-Jacobi-Bellmann Equations...
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