Quantitative Homogenization of Elliptic PDE with Random Oscillatory Boundary Data
William M. Feldman, Inwon C. Kim, Panagiotis E. Souganidis · arXiv (Cornell University) · 2014
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.