Geometric Conditions for Regularity of Viscosity Solution to the Simplest Hamilton-Jacobi Equation
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Abstract
Continuing research in [13] and [14] on well-posedness of the optimal time control problem with a constant convex dynamics in a Hilbert space we adapt one of the regularity conditions obtained there to a slightly more general problem, where nonaffine additive term appears. We prove existence and uniqueness of a minimizer in this problem as well as continuous differentiability of the value function, which can be seen as the viscosity solution to a Hamilton-Jacobi equation, near the boundary.
Keywords
optimal time control problem viscosity solution eikonal equation duality mapping proximal normals proximal regularity Hölder continuity Download
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