Viscosity method for random homogenization of fully nonlinear elliptic equations with highly oscillating obstacles

Abstract

In this article, we establish a viscosity method for random homogenization of an obstacle problem with nondivergence structure. We study the asymptotic behavior of the viscosity solution uε{u}_{\varepsilon } of fully nonlinear equations in a perforated domain with the stationary ergodic condition. By capturing the behavior of the homogeneous solution, analyzing the characters of the corresponding obstacle problem, and finding the capacity-like quantity through the construction of appropriate barriers, we prove that the limit profile uu of uε{u}_{\varepsilon } satisfies a homogenized equation without obstacles.

Keywords

• fully nonlinear operator
• viscosity method
• homogenization
• stationary ergodic
• homogeneous solution
• 35b05
• 35b27
• 74q10