---
_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. <i>SIAM Journal on Mathematical
    Analysis</i>. 2017;49(1):82-114. doi:<a href="https://doi.org/10.1137/16M1070384">10.1137/16M1070384</a>
  apa: Fischer, J. L., &#38; Raithel, C. (2017). Liouville principles and a large-scale
    regularity theory for random elliptic operators on the half-space. <i>SIAM Journal
    on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics .
    <a href="https://doi.org/10.1137/16M1070384">https://doi.org/10.1137/16M1070384</a>
  chicago: Fischer, Julian L, and Claudia Raithel. “Liouville Principles and a Large-Scale
    Regularity Theory for Random Elliptic Operators on the Half-Space.” <i>SIAM Journal
    on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics ,
    2017. <a href="https://doi.org/10.1137/16M1070384">https://doi.org/10.1137/16M1070384</a>.
  ieee: J. L. Fischer and C. Raithel, “Liouville principles and a large-scale regularity
    theory for random elliptic operators on the half-space,” <i>SIAM Journal on Mathematical
    Analysis</i>, 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.” <i>SIAM Journal
    on Mathematical Analysis</i>, vol. 49, no. 1, Society for Industrial and Applied
    Mathematics , 2017, pp. 82–114, doi:<a href="https://doi.org/10.1137/16M1070384">10.1137/16M1070384</a>.
  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'
fulldoi: https://doi.org/10.1137/16M1070384
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'
...