Homogenization of elliptic equations with large random potential

Abstract

We consider an elliptic equation with purely imaginary, highly heterogeneous, and large random potential with a sufficiently rapidly decaying correlation function. We show that its solution is well approximated by the solution to a homogeneous equation with a real-valued homogenized potential as the correlation length of the random medium $\epsilon \to 0$ and estimate the size of the random fluctuations in the setting $d\ge 3$.

14 pages

References in corpus (4)

• Homogenization of a singular random one-dimensional PDE
• Random homogenisation of a highly oscillatory singular potential
• Weak Convergence Approach for Parabolic Equations with Large, Highly Oscillatory, Random Potential
• An invariance principle for Brownian motion in random scenery