The homogenization problem for a nonlinear elliptic equation modelling some physical phenomena set in a periodically heterogeneous medium is studied. Contrary to the usual approach, the coefficients in the equation are supposed to be uncertain functions from a given set of admissible data satisfying suitable monotonicity and continuity conditions. The problem with uncertainties is treated by means of the worst scenario method.
Francu, J., & Nechvatal, L. (2011). Homogenization of monotone problems with uncertain coefficients. Mathematical Modelling and Analysis, 16(3), 432-441. https://doi.org/10.3846/13926292.2011.602725
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