Annealed Calder\'on-Zygmund estimates for elliptic operators with random coefficients on $C^{1}$ domains
| Autor: | Wang, Li, Xu, Qiang |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Concerned with elliptic operators with stationary random coefficients governed by linear or nonlinear mixing conditions and bounded (or unbounded) $C^1$ domains, this paper mainly studies (weighted) annealed Calder\'on-Zygmund estimates, some of which are new even in a periodic setting. Stronger than some classical results derived by a perturbation argument in the deterministic case, our results own a scaling-invariant property, which additionally requires the non-perturbation method (based upon a quantitative homogenization theory and a set of functional analysis techniques) recently developed by M. Joisen and F. Otto \cite{Josien-Otto22}. To handle boundary estimates in certain UMD (unconditional martingale differences) spaces, we hand them over to Shen's real arguments \cite{Shen05, Shen23} instead of using Mikhlin's theorem. As a by-product, we also established ``resolvent estimates''. The potentially attractive part is to show how the two powerful kernel-free methods work together to make the results clean and robust. Comment: 52pages; 2 figures; comments are welcome |
| Databáze: | arXiv |
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