A Liouville theorem for stationary and ergodic ensembles of parabolic systems

Peter Bella, Alberto Chiarini, and Benjamin Fehrman

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Submission date: 14. Jun. 2017
Pages: 37
published in: Probability theory and related fields, 173 (2019) 3/4, p. 759-812 
DOI number (of the published article): 10.1007/s00440-018-0843-z
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Abstract:
A first-order Liouville theorem is obtained for random ensembles of uniformly parabolic systems under the mere qualitative assumptions of stationarity and ergodicity. Furthermore, the paper establishes, almost surely, an intrinsic large-scale $\C^{1,\alpha}$-regularity estimate for caloric functions.