Quantitative Homogenization of Elliptic PDE with Random Oscillatory Boundary Data

2014/08/01 by Feldman, William M., Kim, Inwon, Souganidis, Panagiotis E.
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1408.0254

Abstract

We study the averaging behavior of nonlinear uniformly elliptic partial differential equations with random Dirichlet or Neumann boundary data oscillating on a small scale. Under conditions on the operator, the data and the random media leading to concentration of measure, we prove an almost sure and local uniform homogenization result with a rate of convergence in probability.

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