A Liouville theorem for elliptic systems with degenerate ergodic coefficients

Authors
Bella, Peter Fehrman, Benjamin Otto, Felix
Citation
Bella, Peter et al., A Liouville theorem for elliptic systems with degenerate ergodic coefficients, Annals of applied probability , 28(3), 2018, pp. 1379-1422
Journal title
Annals of applied probability → ACNP
ISSN journal
10505164
Volume
28
Issue
3
Year of publication
2018
Pages
1379 - 1422
Database
ACNP
SICI code
Abstract
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 C1,.-regularity estimate for a-harmonic functions and obtain a first-order Liouville theorem for a-harmonic functions.