{"oa_version":"Submitted Version","issue":"1","quality_controlled":"1","title":"Liouville principles and a large-scale regularity theory for random elliptic operators on the half-space","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1703.04328"}],"language":[{"iso":"eng"}],"intvolume":"        49","publist_id":"6381","date_published":"2017-01-12T00:00:00Z","day":"12","publisher":"Society for Industrial and Applied Mathematics ","year":"2017","abstract":[{"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.","lang":"eng"}],"publication_status":"published","publication":"SIAM Journal on Mathematical Analysis","_id":"1014","doi":"10.1137/16M1070384","author":[{"id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","last_name":"Fischer","orcid":"0000-0002-0479-558X","full_name":"Fischer, Julian L","first_name":"Julian L"},{"last_name":"Raithel","first_name":"Claudia","full_name":"Raithel, Claudia"}],"publication_identifier":{"issn":["00361410"]},"isi":1,"extern":"1","type":"journal_article","date_updated":"2023-09-22T09:43:36Z","volume":49,"oa":1,"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","external_id":{"isi":["000396681800004"]},"status":"public","page":"82 - 114","month":"01","date_created":"2018-12-11T11:49:41Z","citation":{"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.","short":"J.L. Fischer, C. Raithel, SIAM Journal on Mathematical Analysis 49 (2017) 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>.","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>","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.","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>."},"article_processing_charge":"No"}