--- _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' ...