On the Homogenization of the Hamilton-Jacobi Equation

By A. Sorrentino. 2019

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In this article we describe how the celebrated result by Lions, Papanicolau and Varadhan on the Homogenization of Hamilton-Jacobi equation can be extended beyond the Euclidean setting. More specifically, we show how to obtain a homogenization result in the case of Hamiltonians that are invariant under the action of a discrete (virtually) nilpotent group (i.e., with polynomial growth), following ideas of M. Gromov [18] and P. Pansu [28].

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/3302fb452f309fe133892ee1cd1c887e6a617644