Homogenization of Monotone Problems with Uncertain Coefficients

Abstract

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.

Keywords:

• Homogenization
• nonlinear elliptic equation
• uncertain input data
• worst scenario method

AMS Sub ject Classification:

• 35B27
• 35B30
• 35B40
• 35J25
• 35R05
• 49J20