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Viscosity method for random homogenization of fully nonlinear elliptic equations with highly oscillating obstacles
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- Authors
- Issue Date
- 2022-09
- Publisher
- WALTER DE GRUYTER GMBH
- Citation
- Advances in Nonlinear Analysis, Vol.12 No.1, pp.266-303
- 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 u(epsilon) of fully non-linear 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 u of u(epsilon) satisfies a homogenized equation without obstacles.
- ISSN
- 2191-9496
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