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A Liouville theorem for elliptic systems with degenerate ergodic coefficients (1605.00687v1)
Published 2 May 2016 in math.AP and math.PR
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 [Arxiv preprint 1410.4483, 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 subquadratic $a$-harmonic functions.