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 $C^{1,\alpha}$-regularity estimate for $a$-harmonic functions and obtain a first-order Liouville theorem for $a$-harmonic functions.
Citation
Peter Bella. Benjamin Fehrman. Felix Otto. "A Liouville theorem for elliptic systems with degenerate ergodic coefficients." Ann. Appl. Probab. 28 (3) 1379 - 1422, June 2018. https://doi.org/10.1214/17-AAP1332
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