---
_id: '1014'
abstract:
- lang: eng
text: 'We consider the large-scale regularity of solutions to second-order linear
elliptic equations with random coefficient fields. In contrast to previous works
on regularity theory for random elliptic operators, our interest is in the regularity
at the boundary: We consider problems posed on the half-space with homogeneous
Dirichlet boundary conditions and derive an associated C1,α-type large-scale regularity
theory in the form of a corresponding decay estimate for the homogenization-adapted
tilt-excess. This regularity theory entails an associated Liouville-type theorem.
The results are based on the existence of homogenization correctors adapted to
the half-space setting, which we construct-by an entirely deterministic argument-as
a modification of the homogenization corrector on the whole space. This adaption
procedure is carried out inductively on larger scales, crucially relying on the
regularity theory already established on smaller scales.'
article_processing_charge: No
author:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Claudia
full_name: Raithel, Claudia
last_name: Raithel
citation:
ama: Fischer JL, Raithel C. Liouville principles and a large-scale regularity theory
for random elliptic operators on the half-space. SIAM Journal on Mathematical
Analysis. 2017;49(1):82-114. doi:10.1137/16M1070384
apa: Fischer, J. L., & Raithel, C. (2017). Liouville principles and a large-scale
regularity theory for random elliptic operators on the half-space. SIAM Journal
on Mathematical Analysis. Society for Industrial and Applied Mathematics .
https://doi.org/10.1137/16M1070384
chicago: Fischer, Julian L, and Claudia Raithel. “Liouville Principles and a Large-Scale
Regularity Theory for Random Elliptic Operators on the Half-Space.” SIAM Journal
on Mathematical Analysis. Society for Industrial and Applied Mathematics ,
2017. https://doi.org/10.1137/16M1070384.
ieee: J. L. Fischer and C. Raithel, “Liouville principles and a large-scale regularity
theory for random elliptic operators on the half-space,” SIAM Journal on Mathematical
Analysis, vol. 49, no. 1. Society for Industrial and Applied Mathematics ,
pp. 82–114, 2017.
ista: Fischer JL, Raithel C. 2017. Liouville principles and a large-scale regularity
theory for random elliptic operators on the half-space. SIAM Journal on Mathematical
Analysis. 49(1), 82–114.
mla: Fischer, Julian L., and Claudia Raithel. “Liouville Principles and a Large-Scale
Regularity Theory for Random Elliptic Operators on the Half-Space.” SIAM Journal
on Mathematical Analysis, vol. 49, no. 1, Society for Industrial and Applied
Mathematics , 2017, pp. 82–114, doi:10.1137/16M1070384.
short: J.L. Fischer, C. Raithel, SIAM Journal on Mathematical Analysis 49 (2017)
82–114.
date_created: 2018-12-11T11:49:41Z
date_published: 2017-01-12T00:00:00Z
date_updated: 2023-09-22T09:43:36Z
day: '12'
doi: 10.1137/16M1070384
extern: '1'
external_id:
isi:
- '000396681800004'
intvolume: ' 49'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1703.04328
month: '01'
oa: 1
oa_version: Submitted Version
page: 82 - 114
publication: SIAM Journal on Mathematical Analysis
publication_identifier:
issn:
- '00361410'
publication_status: published
publisher: 'Society for Industrial and Applied Mathematics '
publist_id: '6381'
quality_controlled: '1'
status: public
title: Liouville principles and a large-scale regularity theory for random elliptic
operators on the half-space
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 49
year: '2017'
...