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Pré-Publication, Document De Travail Année : 2024

Nonlinear and degenerate discounted approximation in discrete weak KAM theory

Résumé

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 and prove convergence of solutions as the discount factor goes to $0$. We also discuss the uniqueness of the discounted solution. The convergence result is a selection principle for fixed points of a family of nonlinear operators.
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Dates et versions

hal-04501051 , version 1 (12-03-2024)

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Panrui Ni, Maxime Zavidovique. Nonlinear and degenerate discounted approximation in discrete weak KAM theory. 2024. ⟨hal-04501051⟩
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