113 citations · 311 across the 24 of their papers we have counts for
12 papers · 1 filter
Selection of critical solutions in non-monotone vanishing discount problems
Panrui Ni, Jun Yan, Maxime Zavidovique
We study a generalized vanishing discount problem for Hamilton--Jacobi equations without assuming monotonicity either pointwise or in the averaged sense with respect to all Mather…
Convergence/divergence phenomena in the vanishing discount limit of Hamilton-Jacobi equations
Andrea Davini, Panrui Ni, Jun Yan +1
We study the asymptotic behavior of solutions of an equation of the form \begin{equation}\label{abs}\tag{*} G\big(x, D_x u,λu(x)\big) = c_0\qquad\hbox{in } \end{equation} on a c…
Convergence of the solutions of the nonlinear discounted Hamilton-Jacobi equation: The central role of Mather measures
Qinbo Chen, Albert Fathi, Maxime Zavidovique +1
Given a continuous Hamiltonian defined on , where is a closed connected manifold, we study viscosity solutions, $u_λ: M\…
Convergence of solutions for some degenerate discounted Hamilton--Jacobi equations
Maxime Zavidovique
We study solutions of Hamilton--Jacobi equations of the form where is a nonnegative function, a positive constant, a constant and…
Convergence of the solutions of discounted Hamilton--Jacobi systems
Andrea Davini, Maxime Zavidovique
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 specific s…
Random Lax--Oleinik semigroups for Hamilton--Jacobi systems
Andrea Davini, Antonio Siconolfi, Maxime Zavidovique
Following the random approach of Mitake, Siconolfi,Tran and Yamada, we define a Lax--Oleinik formula adapted to evolutive weakly coupled systems of Hamilton--Jacobi equations. It i…
Convergence of the solutions of the discounted equation
Andrea Davini, Albert Fathi, Renato Iturriaga +1
We consider a continuous coercive Hamiltonian on the cotangent bundle of the compact connected manifold which is convex in the momentum. If is the visco…
On the (non) existence of viscosity solutions of multi-time Hamilton-Jacobi equations
Andrea Davini, Maxime Zavidovique
We prove that the multi-time Hamilton-Jacobi equation in general cannot be solved in the viscosity sense, in the non-convex setting, even when the Hamiltonians are in involution.
Aubry sets for weakly coupled systems of Hamilton--Jacobi equations
Andrea Davini, Maxime Zavidovique
We introduce a notion of Aubry set for weakly coupled systems of Hamilton--Jacobi equations on the torus and characterize it as the region where the obstruction to the existence of…
Regularization of subsolutions in discrete weak KAM theory
Patrick Bernard, Maxime Zavidovique
We expose different methods of regularizations of subsolutions in the context of discrete weak KAM theory. They allow to prove the existence and the density of subsolutio…
Weak KAM theoretic aspects for nonregular commuting Hamiltonians
Andrea Davini, Maxime Zavidovique
In this paper we consider the notion of commutation for a pair of continuous and convex Hamiltonians, given in terms of commutation of their Lax- Oleinik semigroups. This is equiva…
Weak KAM for commuting Hamiltonians
Maxime Zavidovique
For two commuting Tonelli Hamiltonians, we recover the commutation of the Lax-Oleinik semi-groups, a result of Barles and Tourin ([BT01]), using a direct geometrical method (Stoke'…