A LIOUVILLE THEOREM FOR ELLIPTIC SYSTEMS WITH DEGENERATE ERGODIC COEFFICIENTS

• 成果类型: Article
• 署名作者: Bella, Peter; Fehrman, Benjamin; Otto, Felix
• 署名单位: Leipzig University; Max Planck Society
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/17-AAP1332
• 发表日期: 2018
• 页码: 1379-1422
• 关键词: stochastic homogenization; invariance-principle; compactness methods; harmonic-functions; EQUATIONS

摘要

We study the behavior of second-order degenerate elliptic systems in divergence form with random coefficients which are stationary and ergodic. Assuming moment bounds like Chiarini and Deuschel (2014) on the coefficient field a and its inverse, we prove an intrinsic large-scale C-1,C-alpha-regularity estimate for a-harmonic functions and obtain a first-order Liouville theorem for a-harmonic functions.