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arXiv · 2103.07638

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

Xifeng Su·Jianlu Zhang
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Abstract

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.

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Xifeng Su, Jianlu Zhang. 2021-03-13. Essential forward weak KAM solution for the convex Hamilton-Jacobi equation. https://arxiv.org/abs/2103.07638

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