A Liouville theorem for elliptic systems with degenerate ergodic coefficients
Peter Bella, Benjamin Fehrman, Félix Otto · The Annals of Applied Probability · 2018
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 $C^{1,\alpha}$-regularity estimate for $a$-harmonic functions and obtain a first-order Liouville theorem for $a$-harmonic functions.