A nearoptimal rate of periodic homogenization for convex HamiltonJacobi equations
Abstract
We consider a HamiltonJacobi equation where the Hamiltonian is periodic in space and coercive and convex in momentum. Combining the representation formula from optimal control theory and a theorem of Alexander, originally proved in the context of firstpassage percolation, we find a rate of homogenization which is within a logfactor of optimal and holds in all dimensions.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.09430
 Bibcode:
 2021arXiv211009430C
 Keywords:

 Mathematics  Analysis of PDEs;
 35F21 (Primary) 35B27 (Secondary)
 EPrint:
 6 pages, comments welcome! (added references and updated introduction)