Corrector theory for elliptic equations in random media with singular Green's function. Application to random boundaries (Q548443)

The authors consider elliptic pseudo-differential equations with random potentials of the form \[ P(x,D)u_\varepsilon + q_\varepsilon(x,x/\varepsilon,\omega)u_\varepsilon = f(x), \] complemented with appropriate boundary conditions. As \(\varepsilon\rightarrow 0\) (\(\varepsilon\) can be interpreted as the correlation length of the random medium) the solution converges to a deterministic solution \(u\) obtained by averaging (homogenization). The authors analyze and estimate the error term \(u_\varepsilon -u\) in the case when the Green function is singular in the sense that it fails to be locally square integrable.