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arxiv: 1303.3219 · v2 · pith:SOTVIWXWnew · submitted 2013-03-13 · 🧮 math.AP · math.DS· math.SG

Viscosity solution of Hamilton-Jacobi equation by a limiting minmax method

classification 🧮 math.AP math.DSmath.SG
keywords solutionviscosityequationhamilton-jacobiminimaxshortercoincideconvex
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For non convex Hamiltonians, the viscosity solution and the more geometric minimax solution of the Hamilton-Jacobi equation do not coincide in general. They are nevertheless related: we show that iterating the minimax procedure during shorter and shorter time intervals one recovers the viscosity solution.

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