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Using the min-plus version of the spectral radius formula, one proves: 1) that the unique eigenvalue of a min-plus eigenvalue problem depends continuously on parameters involved in the kernel defining the problem; 2) that the numerical method introduced by Chou and Griffiths to compute this eigenvalue converges.A toolbox recently developed at I.n.r.i.a. helps to illustrate these results. Frenkel-Kontorova models serve as example. The analogy with homogenization of Hamilton-Jacobi equations is emphasized.

We study a quasiconvex conjugation that transforms the level sum of functions into the pointwise sum of their conjugates and derivenew duality results for the minimization of the max of two quasiconvex functions. Following Barron and al., we show that the levelsum provides quasiconvex viscosity solutions for Hamilton-Jacobi equations in which the initial condition is a general continuousquasiconvex function which is not necessarily Lipschitz or bounded.

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Convergence of numerical methods and parameter dependence of min-plus eigenvalue problems, Frenkel-Kontorova models and homogenizationof Hamilton-Jacobi equations

Duality for the level sum of quasiconvex functions and applications

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Convergence of numerical methods and parameter dependence of min-plus eigenvalue problems, Frenkel-Kontorova models and homogenizationof Hamilton-Jacobi equations

Duality for the level sum of quasiconvex functions and applications