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 …

Given a continuous Hamiltonian H:(x, p, u)↦ H (x, p, u) defined on T⁎ M× R, where M is a
closed connected manifold, we study viscosity solutions, u λ: M→ R, of discounted …

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 …

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 …

We study solutions of Hamilton–Jacobi equations of the form λα (x) uλ (x)+ H (x, Dx uλ)= c,
where α is a nonnegative function, λ a positive constant, ca constant and H a convex …

We study the asymptotic behavior of solutions of an equation of the form\begin
{equation}\label {abs}\tag {*} G\big (x, D_x u,\lambda u (x)\big)= c_0\qquad\hbox {in $ M …

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 …

This paper studies a perturbation problem given by the equation:\begin {equation*} H (x,
d_xu_\lambda,\lambda u_\lambda (x))+\lambda V (x,\lambda)= c\quad\text {in $ M $},\end …

arXiv:2412.06428v1 [math.AP] 9 Dec 2024 Page 1 arXiv:2412.06428v1 [math.AP] 9 Dec 2024
RATE OF CONVERGENCE FOR HOMOGENIZATION OF NONLINEAR WEAKLY COUPLED …

We study a multi-objective variational problem of Herglotz'type with cooperative linear
coupling. We established the associated Euler-Lagrange equations and the characteristic …