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

Abstract

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.

27 pages

References in corpus (2)

• Weak KAM theorem on non compact manifolds
• Pseudographs and Lax-Oleinik semi-group: a geometric and dynamical interpretation

Cited by in corpus (4)

• On the (non) existence of viscosity solutions of multi-time Hamilton-Jacobi equations
• Semi-concave singularities and the Hamilton-Jacobi equation
• Stochastic homogenization for variational solutions of Hamilton-Jacobi equations
• Non-existence of global characteristics for viscosity solutions