Liouville principles and a large-scale regularity theory for random elliptic operators on the half-space Fischer, Julian L ; https://orcid.org/0000-0002-0479-558X Raithel, Claudia 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. Society for Industrial and Applied Mathematics 2017 info:eu-repo/semantics/article doc-type:Article Article http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/1014 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> eng info:eu-repo/semantics/altIdentifier/doi/10.1137/16M1070384 info:eu-repo/semantics/altIdentifier/issn/00361410 info:eu-repo/semantics/altIdentifier/wos/000396681800004 info:eu-repo/semantics/openAccess