activity
20102024
most citedConvergence of the solutions of the discounted equation: the discrete case

112 citations · 114 across the 6 of their papers we have counts for

collaborators

6 papers

math.OC2024

Nonlinear and degenerate discounted approximation in discrete weak KAM theory

Panrui Ni, Maxime Zavidovique

In this paper, we introduce a discrete version of the nonlinear implicit Lax-Oleinik operator. We consider the associated vanishing discount problem with a non-degenerate condition…

math.DS2023

Discrete and Continuous Weak KAM Theory: an introduction through examples and its applications to twist maps

Maxime Zavidovique

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 wea…

math.AP2023

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\…

math.OC2016112 cited

Convergence of the solutions of the discounted equation: the discrete case

Andrea Davini, Albert Fathi, Renato Iturriaga +1

We derive a discrete version of the results of our previous work. If is a compact metric space, a continuous cost function and , the u…

math.DG20102 cited

Ilmanen's Lemma on Insertion of C Functions

Albert Fathi, Maxime Zavidovique

We give a proof of Ilmanen's lemma, which asserts that between a locally semi-convex and a locally semi-concave function it is possible to find a C function.

math.DS2010

Existence of critical subsolutions in discrete weak KAM theory

Maxime Zavidovique

In this article, following a first work of the author, we study critical subsolutions in discrete weak KAM theory. In particular, we establish that if the cost function $c:M \times…