Corrector theory for elliptic equations in random media with singular Green ’ s function . Application to random boundaries

@inproceedings{Bal2010CorrectorTF,
  title={Corrector theory for elliptic equations in random media with singular Green ’ s function . Application to random boundaries},
  author={Guillaume Bal and Wenjia Jing},
  year={2010}
}
We consider the problem of the random fluctuations in the solutions to elliptic PDEs with highly oscillatory random coefficients. In our setting, as the correlation length of the fluctuations tends to zero, the heterogeneous solution converges to a deterministic solution obtained by averaging. When the Green’s function to the unperturbed operator is sufficiently singular (i.e., not square integrable locally), the leading corrector to the averaged solution may be either deterministic or random… CONTINUE READING
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