In this note we revisit the homogenization theory of Hamilton-Jacobi and “viscous”-
Hamilton-Jacobi partial differential equations with convex nonlinearities in stationary ergodic envi-
ronments. We present a new simple proof for the homogenization in probability. The argument uses
some a priori bounds (uniform modulus of continuity) on the solution and the convexity and coer-
civity (growth) of the nonlinearity. It does not rely, however, on the control interpretation formula
of the solution as was the case with all previously known proofs. We also introduce a new formula
for the effective Hamiltonian for Hamilton-Jacobi and “viscous” Hamilton-Jacobi equations.
@article{1274816896,
author = {Lions, Pierre-Louis and Souganidis, Panagiotis E.},
title = {Stochastic homogenization of Hamilon-Jacobi and "viscous"-Hamilton-Jacobi
equations with convex nonlinearities -- Revisited},
journal = {Commun. Math. Sci.},
volume = {8},
number = {1},
year = {2010},
pages = { 627-637},
language = {en},
url = {http://dml.mathdoc.fr/item/1274816896}
}
Lions, Pierre-Louis; Souganidis, Panagiotis E. Stochastic homogenization of Hamilon-Jacobi and "viscous"-Hamilton-Jacobi
equations with convex nonlinearities -- Revisited. Commun. Math. Sci., Tome 8 (2010) no. 1, pp. 627-637. http://gdmltest.u-ga.fr/item/1274816896/