Effective Fronts of Polytope Shapes
Minimax theory and its applications, Tome 5 (2020) no. 2
We study the periodic homogenization of first order front propagations. Based on PDE methods, we provide a simple proof that, for n ≥ 3, the class of centrally symmetric polytopes with rational coordinates and nonempty interior is admissible as effective fronts, which was also established by I. Babenko and F. Balacheff [Sur la forme de la boule unité de la norme stable unidimensionnelle, Manuscripta Math. 119(3) (2006) 347–358] and M. Jotz [Hedlund metrics and the stable norm, Diff. Geometry Appl. 27(4) (2009) 543–550] in the form of stable norms as an extension of Hedlund’s classical result [G. A. Hedlund, Geodesics on a two-dimensional Riemannian manifold with periodic coefficients, Ann. Math. 33 (1932) 719–739]. Besides, we obtain the optimal convergence rate of the homogenization problem for this class.
Mots-clés :
Homogenization, front propagation, effective Hamiltonian, effective fronts, centrally symmetric polytopes, optimal rate of convergence
@article{MTA_2020_5_2_a9,
author = {Wenjia Jing,Hung V. Tran,Yifeng Yu},
title = {Effective {Fronts} of {Polytope} {Shapes}},
journal = {Minimax theory and its applications},
year = {2020},
volume = {5},
number = {2},
url = {http://geodesic.mathdoc.fr/item/MTA_2020_5_2_a9/}
}
Wenjia Jing,Hung V. Tran,Yifeng Yu. Effective Fronts of Polytope Shapes. Minimax theory and its applications, Tome 5 (2020) no. 2. http://geodesic.mathdoc.fr/item/MTA_2020_5_2_a9/