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