--- res: bibo_abstract: - '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.@eng' bibo_authorlist: - foaf_Person: foaf_givenName: Julian L foaf_name: Fischer, Julian L foaf_surname: Fischer foaf_workInfoHomepage: http://www.librecat.org/personId=2C12A0B0-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-0479-558X - foaf_Person: foaf_givenName: Claudia foaf_name: Raithel, Claudia foaf_surname: Raithel bibo_doi: 10.1137/16M1070384 bibo_issue: '1' bibo_volume: 49 dct_date: 2017^xs_gYear dct_identifier: - UT:000396681800004 dct_isPartOf: - http://id.crossref.org/issn/00361410 dct_language: eng dct_publisher: Society for Industrial and Applied Mathematics @ dct_title: Liouville principles and a large-scale regularity theory for random elliptic operators on the half-space@ ...