A LIOUVILLE THEOREM FOR ELLIPTIC SYSTEMS WITH DEGENERATE ERGODIC COEFFICIENTS

作者：Bella Peter^*; Fehrman Benjamin; Otto Felix

来源：Annals of Applied Probability, 2018, 28(3): 1379-1422.

DOI：10.1214/17-AAP1332

• Degenerate elliptic equation
• degenerate elliptic system
• stochastic homogenization
• large-scale regularity
• Liouville theorem

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.

• 出版日期2018-6