{"id":"https://openalex.org/W2625769470","doi":"https://doi.org/10.48550/arxiv.2304.11301","title":"Mixed Problems with a Parameter","display_name":"Mixed Problems with a Parameter","publication_year":2023,"publication_date":"2023-04-22","ids":{"openalex":"https://openalex.org/W2625769470","doi":"https://doi.org/10.48550/arxiv.2304.11301","mag":"2625769470"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2304.11301","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2304.11301","pdf_url":"https://arxiv.org/pdf/2304.11301","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2304.11301","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041110914","display_name":"Alexander A. Shlapunov","orcid":"https://orcid.org/0000-0001-7270-8751","observed_orcids":["https://orcid.org/0000-0001-7270-8751"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shlapunov, Alexander","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5012219293","display_name":"\u041d\u0438\u043a\u043e\u043b\u0430\u0439 \u0422\u0430\u0440\u0445\u0430\u043d\u043e\u0432","orcid":"https://orcid.org/0000-0001-7430-0098","observed_orcids":["https://orcid.org/0000-0001-7430-0098"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tarkhanov, Nikolai","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":null,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12589","display_name":"Differential Equations and Boundary Problems","score":0.989300012588501,"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"}},"topics":[{"id":"https://openalex.org/T12589","display_name":"Differential Equations and Boundary Problems","score":0.989300012588501,"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"}},{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.0031999999191612005,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.002899999963119626,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/mixed-boundary-value-problem","display_name":"mixed boundary value problem","score":0.8009999990463257},{"id":"https://openalex.org/keywords/cauchy-problem","display_name":"Cauchy problem","score":0.9259999990463257},{"id":"https://openalex.org/keywords/elliptic-systems","display_name":"elliptic systems","score":0.9800000190734863},{"id":"https://openalex.org/keywords/uniqueness-of-solutions","display_name":"uniqueness of solutions","score":0.7020000219345093},{"id":"https://openalex.org/keywords/solvability-conditions","display_name":"solvability conditions","score":0.7369999885559082},{"id":"https://openalex.org/keywords/dirac-operator","display_name":"Dirac operator","score":0.9390000104904175},{"id":"https://openalex.org/keywords/helmholtz-equation","display_name":"Helmholtz equation","score":0.9700000286102295},{"id":"https://openalex.org/keywords/smooth-manifolds","display_name":"smooth manifolds","score":0.5889999866485596}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.836190938949585},{"id":"https://openalex.org/C153635880","wikidata":"https://www.wikidata.org/wiki/Q1412436","display_name":"Cauchy problem","level":3,"score":0.6573388576507568},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.5558609366416931},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5546221733093262},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.5346993803977966},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5159995555877686},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.49063101410865784},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.4645867645740509},{"id":"https://openalex.org/C106947605","wikidata":"https://www.wikidata.org/wiki/Q3278575","display_name":"Cauchy boundary condition","level":4,"score":0.45866858959198},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.45679971575737},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.43895289301872253},{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.4262831211090088},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.3092752695083618},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"pmh:oai:arXiv.org:2304.11301","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2304.11301","pdf_url":"https://arxiv.org/pdf/2304.11301","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.503.3696","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.503.3696","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://opus.kobv.de/ubp/volltexte/2008/2667/pdf/2004_02.pdf","raw_type":"text"},{"id":"pmh:oai:kobv.de-opus4-uni-potsdam:13885","doi":null,"is_oa":false,"landing_page_url":"https://publishup.uni-potsdam.de/opus4-ubp/frontdoor/index/index/docId/13885","pdf_url":null,"source":{"id":"https://openalex.org/S4306400594","display_name":"publish.UP (University of Potsdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I176453806","host_organization_name":"University of Potsdam","host_organization_lineage":["https://openalex.org/I176453806"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:kobv.de-opus4-uni-potsdam:14006","doi":null,"is_oa":false,"landing_page_url":"https://publishup.uni-potsdam.de/opus4-ubp/frontdoor/index/index/docId/14006","pdf_url":null,"source":{"id":"https://openalex.org/S4306400594","display_name":"publish.UP (University of Potsdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I176453806","host_organization_name":"University of Potsdam","host_organization_lineage":["https://openalex.org/I176453806"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"book"},{"id":"pmh:oai:kobv.de-opus4-uni-potsdam:2466","doi":null,"is_oa":false,"landing_page_url":"https://nbn-resolving.org/urn:nbn:de:kobv:517-opus-26677","pdf_url":null,"source":{"id":"https://openalex.org/S4306400594","display_name":"publish.UP (University of Potsdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I176453806","host_organization_name":"University of Potsdam","host_organization_lineage":["https://openalex.org/I176453806"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"publishedVersion"},{"id":"doi:10.48550/arxiv.2304.11301","doi":"https://doi.org/10.48550/arxiv.2304.11301","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2304.11301","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"},{"id":"mag:2625769470","doi":null,"is_oa":false,"landing_page_url":"https://publishup.uni-potsdam.de/files/2466/2004_02.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2304.11301","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2304.11301","pdf_url":"https://arxiv.org/pdf/2304.11301","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320875","display_name":"Deutscher Akademischer Austauschdienst","ror":"https://ror.org/039djdh30"},{"id":"https://openalex.org/F4320321079","display_name":"Russian Foundation for Basic Research","ror":"https://ror.org/02mh1ke95"},{"id":"https://openalex.org/F4320322480","display_name":"Universit\u00e4t Potsdam","ror":"https://ror.org/03bnmw459"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2625769470.pdf","grobid_xml":"https://content.openalex.org/works/W2625769470.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W120052141","https://openalex.org/W339436875","https://openalex.org/W374450226","https://openalex.org/W599673803","https://openalex.org/W1592003393","https://openalex.org/W1992324689","https://openalex.org/W2022337355","https://openalex.org/W3021722416"],"related_works":["https://openalex.org/W339436875","https://openalex.org/W1967190854","https://openalex.org/W2027295821","https://openalex.org/W120052141","https://openalex.org/W2211307173","https://openalex.org/W2057792244","https://openalex.org/W1967041691","https://openalex.org/W2735058722","https://openalex.org/W1539548302","https://openalex.org/W2112690082","https://openalex.org/W2352782509","https://openalex.org/W3135715222","https://openalex.org/W3206684632","https://openalex.org/W3004038115","https://openalex.org/W2951056925","https://openalex.org/W2088306641","https://openalex.org/W66558469","https://openalex.org/W2069592387","https://openalex.org/W2141602325","https://openalex.org/W2147454575"],"abstract_inverted_index":{"Let":[0],"$X$":[1,15],"be":[2,9],"a":[3,37,46,53,66,118,140,172],"smooth":[4,17],"$n\\,$-dimensional":[5],"manifold":[6],"and":[7,89,147],"$D$":[8,33],"an":[10,26,84,148],"open":[11],"connected":[12],"set":[13,39],"in":[14,32,75,83,105,124,159],"with":[16,34],"boundary":[18,68,176],"$\\partial":[19,71],"D$.":[20],"Perturbing":[21],"the":[22,60,90,99,102,108,115,121,129,132,144,160,167,179],"Cauchy":[23,103,122,145],"problem":[24,104,123,146],"for":[25,143,156,178],"elliptic":[27],"system":[28],"$Au":[29],"=":[30],"f$":[31],"data":[35],"on":[36,52,70],"closed":[38],"$\\iG":[40],"\\subset":[41],"\\partial":[42],"D$":[43],"we":[44,170],"obtain":[45,171],"family":[47,92,133,173],"of":[48,78,96,101,117,131,151,174],"mixed":[49,61,175],"problems":[50,62,177],"depending":[51],"small":[54],"parameter":[55],"$\\varepsilon":[56],">":[57],"0$.":[58],"Although":[59],"are":[63,164],"subject":[64],"to":[65,120,128],"non-coercive":[67],"condition":[69,142],"D":[72],"\\setminus":[73],"\\iG$":[74],"general,":[76],"each":[77],"them":[79],"is":[80,126],"uniquely":[81],"solvable":[82],"appropriate":[85],"Hilbert":[86],"space":[87,162],"$\\cD_{T}$":[88,106,125],"corresponding":[91],"$\\{":[93,134],"u_{\\varepsilon}":[94,135],"\\}$":[95],"solutions":[97],"approximates":[98],"solution":[100,109,119],"whenever":[107],"exists.":[110],"We":[111,137],"also":[112],"prove":[113],"that":[114],"existence":[116],"equivalent":[127],"boundedness":[130],"\\}$.":[136],"thus":[138],"derive":[139],"solvability":[141],"effective":[149],"method":[150],"constructing":[152],"its":[153],"solution.":[154],"Examples":[155],"Dirac":[157],"operators":[158],"Euclidean":[161],"$\\R^n$":[163],"considered.":[165],"In":[166],"latter":[168],"case":[169],"Helmholtz":[180],"equation.":[181]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2026-10-08T09:06:37.294493","created_date":"2025-10-10T00:00:00"}
