{"id":"https://openalex.org/W7165654984","doi":"https://doi.org/10.48550/arxiv.2606.21375","title":"Inverse Source Problems for a Class of Fractional Elliptic Equations with Singular Coefficients","display_name":"Inverse Source Problems for a Class of Fractional Elliptic Equations with Singular Coefficients","publication_year":2026,"publication_date":"2026-06-19","ids":{"openalex":"https://openalex.org/W7165654984","doi":"https://doi.org/10.48550/arxiv.2606.21375"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.21375","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.21375","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.21375","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5139149800","display_name":"Zewen Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Zewen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139197496","display_name":"Liang Guo","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Guo, Liang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139143610","display_name":"Shufang Qiu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Qiu, Shufang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5139209620","display_name":"Bin Wu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wu, Bin","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":false,"cited_by_count":0,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9894999861717224,"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"}},"topics":[{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9894999861717224,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.0017999999690800905,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T11739","display_name":"Microwave Imaging and Scattering Analysis","score":0.001500000013038516,"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/tikhonov-regularization","display_name":"Tikhonov regularization","score":0.913100004196167},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.6610000133514404},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.6155999898910522},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.564300000667572},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.5217999815940857},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.459199994802475},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.40849998593330383}],"concepts":[{"id":"https://openalex.org/C152442038","wikidata":"https://www.wikidata.org/wiki/Q2778212","display_name":"Tikhonov regularization","level":3,"score":0.913100004196167},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.758899986743927},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6610000133514404},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.6155999898910522},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.564300000667572},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5217999815940857},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48590001463890076},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4708000123500824},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.459199994802475},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.40849998593330383},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.35429999232292175},{"id":"https://openalex.org/C76134657","wikidata":"https://www.wikidata.org/wiki/Q370634","display_name":"Generalized inverse","level":3,"score":0.33660000562667847},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.3212999999523163},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.3149000108242035},{"id":"https://openalex.org/C141718189","wikidata":"https://www.wikidata.org/wiki/Q7309628","display_name":"Regularization perspectives on support vector machines","level":4,"score":0.2694999873638153},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.26739999651908875},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.2621000111103058},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.25619998574256897}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.21375","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.21375","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.21375","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.21375","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"An":[0],"inverse":[1,39],"source":[2,70,121,127,132],"problem":[3],"for":[4,66,86,146],"a":[5,24,41,49,94,97],"class":[6],"of":[7,32,100],"fractional":[8],"elliptic":[9],"equations":[10],"with":[11,53],"singular":[12],"coefficients":[13],"is":[14,27,35,46],"investigated":[15],"in":[16,48],"this":[17,58],"paper.":[18],"For":[19,37],"the":[20,30,33,38,68,72,78,87,101,112,125,138],"corresponding":[21],"direct":[22],"problem,":[23,40],"formal":[25],"solution":[26,34],"derived":[28,91],"and":[29,77,96,143,149],"well-posedness":[31],"established.":[36],"H\u00f6lder-type":[42],"conditional":[43],"stability":[44,59],"estimate":[45],"obtained":[47],"Hilbert":[50],"scale":[51],"associated":[52],"exponential":[54,79],"operators.":[55],"Based":[56],"on":[57],"framework,":[60],"two":[61],"regularization":[62,75,82,102],"methods":[63,114,140],"are":[64,90,115],"proposed":[65,113,139],"reconstructing":[67],"unknown":[69],"term:":[71],"exponential-type":[73,131],"Tikhonov":[74],"method":[76],"quasi-boundary":[80],"value":[81],"method.":[83],"Convergence":[84],"estimates":[85],"regularized":[88],"solutions":[89],"under":[92,154],"both":[93,147],"priori":[95],"posteriori":[98],"choices":[99],"parameter.":[103],"In":[104],"addition,":[105],"finite-dimensional":[106],"spectral":[107],"approximation":[108],"results":[109],"show":[110],"that":[111,137],"also":[116],"applicable":[117],"to":[118,128],"general":[119],"square-integrable":[120],"terms,":[122],"without":[123],"requiring":[124],"exact":[126],"satisfy":[129],"an":[130],"condition.":[133],"Numerical":[134],"experiments":[135],"demonstrate":[136],"provide":[141],"stable":[142],"accurate":[144],"reconstructions":[145],"smooth":[148,151],"piecewise":[150],"sources":[152],"even":[153],"low":[155],"signal-to-noise":[156],"ratio":[157],"conditions.":[158]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-06-24T00:00:00"}