A Liouville theorem for stationary and ergodic ensembles of parabolic systems

Peter Bella; Alberto Chiarini; Benjamin Fehrman

doi:10.1007/s00440-018-0843-z

A Liouville theorem for stationary and ergodic ensembles of parabolic systems

Peter Bella, Alberto Chiarini, Benjamin Fehrman (Corresponding author)

Onderzoeksoutput: Bijdrage aan tijdschrift › Tijdschriftartikel › Academic › peer review

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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 ^, ^α -regularity estimate for caloric functions.

Originele taal-2	Engels
Pagina's (van-tot)	759-812
Aantal pagina's	54
Tijdschrift	Probability Theory and Related Fields
Volume	173
Nummer van het tijdschrift	3-4
DOI's	https://doi.org/10.1007/s00440-018-0843-z
Status	Gepubliceerd - 5 apr. 2019

Financiering

Peter Bella is supported by the German Science Foundation DFG in context of the Emmy Noether Junior Research Group BE 5922/1-1. Alberto Chiarini is supported by LabEx Archiméd. Benjamin Fehrman is supported by the National Science Foundation Mathematical Sciences Postdoctoral Research Fellowship under Grant No. 1502731.

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title = "A Liouville theorem for stationary and ergodic ensembles of parabolic systems",

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 , α -regularity estimate for caloric functions. ",

keywords = "Large-scale regularity, Liouville theorem, Parabolic equation, Parabolic system, Stochastic homogenization",

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AU - Fehrman, Benjamin

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KW - Large-scale regularity

KW - Liouville theorem

KW - Parabolic equation

KW - Parabolic system

KW - Stochastic homogenization

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A Liouville theorem for stationary and ergodic ensembles of parabolic systems

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