Herglotz’ Generalized Variational Principle and Contact Type Hamilton-Jacobi Equations |
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We develop an elementary method to give a Lipschitz estimate for the minimizers in the
problem of Herglotz'variational principle proposed in the paper (P. Cannarsa, W. Cheng, K …

We study the vanishing discount problem for a nonlinear monotone system of Hamilton–
Jacobi equations. This continues the first author's investigation on the vanishing discount …

Following the random approach of [1], we define a Lax–Oleinik formula adapted to evolutive
weakly coupled systems of Hamilton–Jacobi equations. It is reminiscent of the …

We consider a weakly coupled system of discounted Hamilton–Jacobi equations set on a
closed Riemannian manifold. We prove that the corresponding solutions converge to a …

We establish a convergence theorem for the vanishing discount problem for a weakly
coupled system of Hamilton-Jacobi equations. The crucial step is the introduction of Mather …

The aim of these notes is to present a self contained account of discrete weak KAM theory.
Put aside the intrinsic elegance of this theory, it is also a toy model for classical weak KAM …

In this paper, we study solutions for a weakly coupled system of eikonal equations arising in
an optimal path-planning problem with random breakdown. The model considered takes …

Here, we prove the existence of solutions to first-order mean-field games (MFGs) arising in
optimal switching. First, we use the penalization method to construct approximate solutions …

These notes are based on the two courses given by the authors at the summer school on
“PDE and Applied Mathematics” at Vietnam Institute for Advanced Study in Mathematics …