Non-uniformly parabolic equations and applications to the random conductance model

• 成果类型: Article
• 署名作者: Bella, Peter; Schaeffner, Mathias
• 署名单位: Dortmund University of Technology
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-021-01081-1
• 发表日期: 2022
• 页码: 353-397
• 关键词: quenched invariance-principles; local limit-theorems; random-walks; quantitative homogenization; harnack inequalities; percolation; REGULARITY

摘要

We study local regularity properties of linear, non-uniformly parabolic finite-difference operators in divergence form related to the random conductance model on Z(d). In particular, we provide an oscillation decay assuming only certain summability properties of the conductances and their inverse, thus improving recent results in that direction. As an application, we provide a local limit theorem for the random walk in a random degenerate and unbounded environment.