{"id":"https://openalex.org/W3164422515","doi":"https://doi.org/10.3934/nhm.2023079","title":"Stochastic homogenization on perforated domains \u2160 \u2013 Extension Operators","display_name":"Stochastic homogenization on perforated domains \u2160 \u2013 Extension Operators","publication_year":2023,"publication_date":"2023-01-01","ids":{"openalex":"https://openalex.org/W3164422515","doi":"https://doi.org/10.3934/nhm.2023079","mag":"3164422515"},"language":"en","primary_location":{"id":"doi:10.3934/nhm.2023079","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3934/nhm.2023079","pdf_url":null,"source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks and Heterogeneous Media","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"http://dx.doi.org/10.3934/nhm.2023079","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074099761","display_name":"Martin Heida","orcid":"https://orcid.org/0000-0002-7242-8175"},"institutions":[{"id":"https://openalex.org/I4210092021","display_name":"Weierstrass Institute for Applied Analysis and Stochastics","ror":"https://ror.org/00h1x4t21","country_code":"DE","type":"facility","lineage":["https://openalex.org/I315704651","https://openalex.org/I4210092021"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Martin Heida","raw_affiliation_strings":["WIAS Berlin, Mohrenstr. 39, 10117 Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"WIAS Berlin, Mohrenstr. 39, 10117 Berlin, Germany","institution_ids":["https://openalex.org/I4210092021"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5074099761"],"corresponding_institution_ids":["https://openalex.org/I4210092021"],"apc_list":null,"apc_paid":null,"fwci":0.4034,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.6071077,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"18","issue":"4","first_page":"1820","last_page":"1897"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11558","display_name":"Composite Material Mechanics","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/homogenization","display_name":"Homogenization (climate)","score":0.7860556840896606},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.7285212278366089},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7272725105285645},{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.645711362361908},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.631318211555481},{"id":"https://openalex.org/keywords/ergodic-theory","display_name":"Ergodic theory","score":0.6253677010536194},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.46308308839797974},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4288621246814728}],"concepts":[{"id":"https://openalex.org/C2778722038","wikidata":"https://www.wikidata.org/wiki/Q17030643","display_name":"Homogenization (climate)","level":3,"score":0.7860556840896606},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.7285212278366089},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7272725105285645},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.645711362361908},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.631318211555481},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.6253677010536194},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.46308308839797974},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4288621246814728},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C130217890","wikidata":"https://www.wikidata.org/wiki/Q47041","display_name":"Biodiversity","level":2,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3934/nhm.2023079","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3934/nhm.2023079","pdf_url":null,"source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks and Heterogeneous Media","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:a943b22956d84d7eb0d86bfde422535c","is_oa":true,"landing_page_url":"https://doaj.org/article/a943b22956d84d7eb0d86bfde422535c","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Networks and Heterogeneous Media, Vol 18, Iss 4, Pp 1820-1897 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3934/nhm.2023079","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3934/nhm.2023079","pdf_url":null,"source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks and Heterogeneous Media","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.5199999809265137,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W26393435","https://openalex.org/W1500863000","https://openalex.org/W1547249381","https://openalex.org/W1569071183","https://openalex.org/W1593939129","https://openalex.org/W1651248654","https://openalex.org/W1964145410","https://openalex.org/W1967809206","https://openalex.org/W1968063396","https://openalex.org/W1994521362","https://openalex.org/W2022845172","https://openalex.org/W2023324267","https://openalex.org/W2052197092","https://openalex.org/W2064236519","https://openalex.org/W2073338849","https://openalex.org/W2085424258","https://openalex.org/W2126881652","https://openalex.org/W2169670466","https://openalex.org/W2507648347","https://openalex.org/W2528221652","https://openalex.org/W2618243271","https://openalex.org/W2972646285","https://openalex.org/W3021722416","https://openalex.org/W3036627574","https://openalex.org/W3094952156","https://openalex.org/W3103811994","https://openalex.org/W3118525948","https://openalex.org/W4205976284","https://openalex.org/W4255530919","https://openalex.org/W4287394275"],"related_works":["https://openalex.org/W2390585021","https://openalex.org/W50969306","https://openalex.org/W2104620528","https://openalex.org/W2121543990","https://openalex.org/W2402800040","https://openalex.org/W2000020320","https://openalex.org/W412641959","https://openalex.org/W4252969132","https://openalex.org/W1981078319","https://openalex.org/W2008917324"],"abstract_inverted_index":{"&lt;abstract&gt;&lt;p&gt;In":[0],"this":[1],"first":[2],"part":[3],"of":[4,7,19,49,99,105,110,142,190,206,212],"a":[5,13,133,224,255,261],"series":[6],"3":[8],"papers,":[9],"we":[10,93,135,165,220,231,267],"set":[11],"up":[12],"framework":[14],"to":[15,40,77,160,175,186,202,209,217,249,260],"study":[16,53],"the":[17,36,46,83,95,100,106,111,118,130,143,178,188,191,194,204,210,213,228,250,271],"existence":[18],"uniformly":[20],"bounded":[21],"extension":[22,66,147,207],"and":[23,52,126,139,148,163,182,193,230,238,259],"trace":[24,149],"operators":[25,67,150,208],"for":[26,117,127,153,233,265],"$":[27,73,76,78,81,86,96,107,122,171],"W^{1,":[28,74,79],"p}":[29,75],"$-functions":[30],"on":[31,129,254],"randomly":[32],"perforated":[33],"domains,":[34],"where":[35],"geometry":[37,192],"is":[38],"assumed":[39],"be":[41,69],"stationary":[42,54],"ergodic.":[43],"We":[44,241],"drop":[45],"classical":[47],"assumption":[48],"minimally":[50],"smoothness":[51],"geometries":[55],"which":[56,266],"have":[57],"no":[58],"global":[59],"John":[60],"regularity.":[61],"For":[62],"such":[63],"geometries,":[64],"uniform":[65],"can":[68,268],"defined":[70],"only":[71],"from":[72],"r}":[80],"with":[82],"strict":[84],"inequality":[85],"r":[87],"&amp;lt;":[88],"p":[89],"$.":[90],"In":[91,158,215],"particular,":[92],"estimate":[94,270],"L^{r}":[97],"$-norm":[98,109],"extended":[101],"gradient":[102],"in":[103,155],"terms":[104],"L^{p}":[108],"original":[112],"gradient.":[113],"Similar":[114],"relations":[115],"hold":[116],"symmetric":[119],"gradients":[120],"(for":[121],"{\\mathbb{R}^{d}}":[123],"$-valued":[124],"functions)":[125],"traces":[128],"boundary.":[131],"As":[132],"byproduct":[134],"obtain":[136],"some":[137],"Poincar\u00e9":[138],"Korn":[140],"inequalities":[141],"same":[144],"spirit.&lt;/p&gt;":[145],"&lt;p&gt;Such":[146],"are":[151,200],"important":[152],"compactness":[154],"stochastic":[156],"homogenization.":[157],"contrast":[159,216],"former":[161,218],"approaches":[162,219],"results,":[164],"use":[166],"very":[167],"weak":[168],"assumptions:":[169],"local":[170,179],"(\\delta,":[172],"M)":[173],"$-regularity":[174],"quantify":[176,187],"statistically":[177],"Lipschitz":[180,236],"regularity":[181],"isotropic":[183],"cone":[184],"mixing":[185],"density":[189],"mesoscopic":[195],"properties.":[196],"These":[197],"two":[198],"properties":[199],"sufficient":[201],"reduce":[203],"problem":[205],"connectivity":[211,272],"geometry.":[214],"do":[221],"not":[222],"require":[223],"minimal":[225],"distance":[226],"between":[227],"inclusions":[229],"allow":[232],"globally":[234],"unbounded":[235],"constants":[237],"percolating":[239],"holes.":[240],"will":[242],"illustrate":[243],"our":[244],"method":[245],"by":[246],"applying":[247],"it":[248],"Boolean":[251],"model":[252],"based":[253],"Poisson":[256],"point":[257],"process":[258],"Delaunay":[262],"pipe":[263],"process,":[264],"explicitly":[269],"terms.&lt;/p&gt;&lt;/abstract&gt;":[273]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2025-12-25T23:11:45.687758","created_date":"2025-10-10T00:00:00"}
