{"id":"https://openalex.org/W2166861110","doi":"https://doi.org/10.1137/130948999","title":"Exact Scaling Exponents in Korn and Korn-Type Inequalities for Cylindrical Shells","display_name":"Exact Scaling Exponents in Korn and Korn-Type Inequalities for Cylindrical Shells","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2166861110","doi":"https://doi.org/10.1137/130948999","mag":"2166861110"},"language":"en","primary_location":{"id":"doi:10.1137/130948999","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130948999","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040134907","display_name":"Yury Grabovsky","orcid":"https://orcid.org/0000-0001-5237-6753"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yury Grabovsky","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5015430983","display_name":"Davit Harutyunyan","orcid":"https://orcid.org/0000-0002-8685-2778"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Davit Harutyunyan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.2163,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.92367644,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"46","issue":"5","first_page":"3277","last_page":"3295"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9998000264167786,"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/T11366","display_name":"Elasticity and Material Modeling","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7703534364700317},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.7664942741394043},{"id":"https://openalex.org/keywords/ansatz","display_name":"Ansatz","score":0.7388838529586792},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.7143006324768066},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6524286866188049},{"id":"https://openalex.org/keywords/shell","display_name":"Shell (structure)","score":0.5488052368164062},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5091239809989929},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4985060691833496},{"id":"https://openalex.org/keywords/buckling","display_name":"Buckling","score":0.49060240387916565},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.47161322832107544},{"id":"https://openalex.org/keywords/rod","display_name":"Rod","score":0.44916045665740967},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.19029474258422852},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.18979960680007935},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.06383314728736877}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7703534364700317},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.7664942741394043},{"id":"https://openalex.org/C130979935","wikidata":"https://www.wikidata.org/wiki/Q568954","display_name":"Ansatz","level":2,"score":0.7388838529586792},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.7143006324768066},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6524286866188049},{"id":"https://openalex.org/C2781052500","wikidata":"https://www.wikidata.org/wiki/Q2230313","display_name":"Shell (structure)","level":2,"score":0.5488052368164062},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5091239809989929},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4985060691833496},{"id":"https://openalex.org/C85476182","wikidata":"https://www.wikidata.org/wiki/Q693104","display_name":"Buckling","level":2,"score":0.49060240387916565},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.47161322832107544},{"id":"https://openalex.org/C162184086","wikidata":"https://www.wikidata.org/wiki/Q505544","display_name":"Rod","level":3,"score":0.44916045665740967},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.19029474258422852},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.18979960680007935},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.06383314728736877},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C142724271","wikidata":"https://www.wikidata.org/wiki/Q7208","display_name":"Pathology","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C204787440","wikidata":"https://www.wikidata.org/wiki/Q188504","display_name":"Alternative medicine","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/130948999","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130948999","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[{"id":"https://openalex.org/G3933845068","display_name":"Stability and macroscopic properties of heterogeneous media","funder_award_id":"1008092","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W105606343","https://openalex.org/W128409572","https://openalex.org/W613838126","https://openalex.org/W650857255","https://openalex.org/W1587069887","https://openalex.org/W1974948403","https://openalex.org/W1976444058","https://openalex.org/W1976496016","https://openalex.org/W1982822457","https://openalex.org/W1991637191","https://openalex.org/W2015176885","https://openalex.org/W2022091363","https://openalex.org/W2022382371","https://openalex.org/W2028023659","https://openalex.org/W2030579135","https://openalex.org/W2038282829","https://openalex.org/W2063376474","https://openalex.org/W2068711657","https://openalex.org/W2072227882","https://openalex.org/W2083422172","https://openalex.org/W2093237580","https://openalex.org/W2095328623","https://openalex.org/W2105340951","https://openalex.org/W2140687447","https://openalex.org/W2148262800","https://openalex.org/W2160446307","https://openalex.org/W2170315721","https://openalex.org/W2274054356","https://openalex.org/W2322166453","https://openalex.org/W2322458600","https://openalex.org/W2323745889","https://openalex.org/W2917827752","https://openalex.org/W3104069888"],"related_works":["https://openalex.org/W142639359","https://openalex.org/W14851375","https://openalex.org/W75985283","https://openalex.org/W2088747367","https://openalex.org/W2037773790","https://openalex.org/W2000835246","https://openalex.org/W2028184944","https://openalex.org/W1979707339","https://openalex.org/W3103496316","https://openalex.org/W4323657827"],"abstract_inverted_index":{"Understanding":[0],"asymptotics":[1],"of":[2,16,18,31,38,49,60,83],"gradient":[3,10,51],"components":[4,48],"in":[5,52,76],"relation":[6],"to":[7],"the":[8,14,27,32,50,61,73,80],"symmetrized":[9],"is":[11,68],"important":[12],"for":[13,46],"analysis":[15],"buckling":[17],"slender":[19],"structures.":[20],"For":[21],"circular":[22],"cylindrical":[23,53],"shells":[24],"we":[25],"obtain":[26],"exact":[28],"scaling":[29],"exponent":[30],"Korn":[33],"constant":[34],"as":[35],"a":[36],"function":[37],"shell's":[39],"thickness.":[40],"Equally":[41],"sharp":[42],"results":[43],"are":[44],"obtained":[45],"individual":[47],"coordinates.":[54],"We":[55],"also":[56],"derive":[57],"an":[58],"analogue":[59],"Kirchhoff":[62],"ansatz,":[63],"whose":[64],"most":[65],"prominent":[66],"feature":[67],"its":[69],"singular":[70],"dependence":[71],"on":[72],"slenderness":[74],"parameter,":[75],"marked":[77],"contrast":[78],"with":[79],"classical":[81],"case":[82],"plates":[84],"and":[85],"rods.":[86]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}