A Liouville theorem for elliptic systems with degenerate ergodic coefficients

Peter Bella, Benjamin Fehrman, and Felix Otto

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Submission date: 08. Jul. 2016
Pages: 20
published in: The annals of applied probability, 28 (2018) 3, p. 1379-1422 
DOI number (of the published article): 10.1214/17-AAP1332
Bibtex
MSC-Numbers: 35B53, 35B65, 35J70, 60H25, 60K37
Keywords and phrases: degenerate elliptic equation, degenerate elliptic system, stochastic homogenization, large-scale regularity, liouville theorem
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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,α-regularity estimate for a-harmonic functions and obtain a first-order Liouville theorem for subquadratic a-harmonic functions.