Essential forward weak KAM solution for the convex Hamilton-Jacobi equation

Jianlu Zhang; Xifeng SU

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Essential forward weak KAM solution for the convex Hamilton-Jacobi equation

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arxiv 2103.07638 v1 pith:Z4OD4FF2 submitted 2021-03-13 math.DS

Essential forward weak KAM solution for the convex Hamilton-Jacobi equation

Xifeng Su , Jianlu Zhang This is my paper

classification math.DS

keywords solutionconvexforwardweakapproachclosedcoercivecompact

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For a convex, coercive continuous Hamiltonian on a compact closed Riemannian manifold $M$, we construct a unique forward weak KAM solution of \[ H(x, d_x u)=c(H) \] by a vanishing discount approach, where $c(H)$ is the Ma\~n\'e critical value. We also discuss the dynamical significance of such a special solution.

Essential forward weak KAM solution for the convex Hamilton-Jacobi equation

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