Journal
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
Volume 117, Issue -, Pages 221-262Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.matpur.2018.03.005
Keywords
Homogenization; Hamilton-Jacobi equations; Viscosity solutions; Weak KAM theory; Random media
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Funding
- ANR (Agence Nationale de la Recherche) [ANR-12-BS01-0008-01]
- National Science Foundation [DMS-1266383, DMS-1600129]
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This paper is concerned with the behavior of the ergodic constant associated with convex and superlinear Hamilton-Jacobi equation in a periodic environment which is perturbed either by medium with increasing period or by a random Bernoulli perturbation with small parameter. We find a first order Taylor's expansion for the ergodic constant which depends on the dimension d. When d = 1 the first order term is non trivial, while for all d >= 2 it is always 0. Although such questions have been looked at in the context of linear uniformly elliptic homogenization, our results are the first of this kind in nonlinear settings. Our arguments, which rely on viscosity solutions and the weak KAM theory, also raise several new and challenging questions. (C) 2018 Elsevier Masson SAS. All rights reserved.
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