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