Existence and uniqueness of correctors for nonlinear homogenization in uniformly local Sobolev spaces
Abstract
Abstract We prove the existence and uniqueness of correctors for nonlinear homogenization problems associated with monotone operators of p -growth. The corrector equation is posed in the full space $$\mathbb {R}^d$$ , as required in the non-periodic deterministic setting, and is solved within the framework of uniformly local Sobolev spaces. Our method relies on a localization procedure based on a sequence of increasing balls combined with the large mass trick, together with Caccioppoli-type estimates to establish compactness and stability. The results provide a foundation for extending deterministic homogenization theory beyond the periodic framework, ensuring that correctors exist and are uniquely defined in general heterogeneous media.
Fields of Study & Subjects
Advanced Mathematical Modeling in Engineering
Nonlinear Partial Differential Equations
Composite Material Mechanics
Publication details
- Journal / source
- The Journal of Analysis
- Publisher
- Springer Science and Business Media LLC
- Volume
- 34
- Issue
- 5
- Pages
- 3437-3456
- Publication date
- 20 July 2026
- Language
- EN