{"id":{"repo_id":"wichita-thes","oai_identifier":"oai:null:10057/25700"},"canonical_url":"https://search.dev.ndltd.org/etd/wichita-thes/oai:null:10057/25700","repository":{"repo_id":"wichita-thes","name":"Wichita State University","base_url":"https://soar.wichita.edu/oai/request"},"display":{"title":"Continuation from discrete sets and inverse problems","abstract":"It is well known that every smooth surface S is at least locally generated by the Dirac equation with real potential. In this dissertation, we study the inverse problem of recovering this potential and surface based on given Gaussian curvature and discrete Cauchy data on $z_n$ assuming that S is a Willmore surface $r : \\mathbb{D} \\rightarrow R^3$ We reduce this problem to several problems of the type: $|\\partial \\bar{u}|\\leq a|u|,$ $\\forall{z}\\in\\mathbb{D},$ $n = 1,2,3$ with given discrete Cauchy data on {$z_n$} For sequence $z_n$ we assume Blaschke condition $\\displaystyle\\sum\\limits_{n=1}^{\\infty}(1|-|z_n|)=\\infty$ Our main tool is Carleman estimates.","abstract_html":"It is well known that every smooth surface S is at least locally generated by the Dirac equation with real potential. In this dissertation, we study the inverse problem of recovering this potential and surface based on given Gaussian curvature and discrete Cauchy data on <span class=\"etd-inline-math\">z<sub>n</sub></span> assuming that S is a Willmore surface <span class=\"etd-inline-math\">r : \\mathbb{D} \\rightarrow R<sup>3</sup></span> We reduce this problem to several problems of the type: $|\\partial \\bar{u}|\\leq a|u|,$ $\\forall{z}\\in\\mathbb{D},$ $n = 1,2,3$ with given discrete Cauchy data on {<span class=\"etd-inline-math\">z<sub>n</sub></span>} For sequence <span class=\"etd-inline-math\">z<sub>n</sub></span> we assume Blaschke condition <span class=\"etd-inline-math\">\\displaystyle\\sum\\limits<sub>n=1</sub><sup>\\infty</sup>(1|-|z<sub>n</sub>|)=\\infty</span> Our main tool is Carleman estimates.","abstract_has_math":true,"creators":["Domme, Cristina Camelia"],"institution":"Wichita State University","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Bukhgeym, Alexander L."],"committee_chairs":[],"committee_members":[],"year":2023,"date_issued":"2023-07","date_published":"2023-07","updated_at":"2026-08-21T16:50:43Z","subjects":[],"languages":["en_US"],"rights":["© Copyright 2023 by Cristina C. Domme All Rights Reserved"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["d23020s"],"render_values":[{"text":"d23020s","href":null,"code":true}]}]},"links":{"outbound_url":"https://soar.wichita.edu/handle/10057/25700","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"source_record":{"url":"https://soar.wichita.edu/oai/request?verb=GetRecord&metadataPrefix=dim&identifier=oai%3Anull%3A10057%2F25700","prefix":"dim"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Bukhgeym, Alexander L."]},{"key":"dc:creator","label":"Author","values":["Domme, Cristina Camelia"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2023-08-29T18:43:50Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2023-08-29T18:43:50Z"]},{"key":"dc:date.issued","label":"Date","values":["2023-07"]},{"key":"dc:publisher","label":"Institution","values":["Wichita State University"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en_US"]},{"key":"dc:rights","label":"Dc Rights","values":["© Copyright 2023 by Cristina C. Domme All Rights Reserved"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["d23020s"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://soar.wichita.edu/handle/10057/25700"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Thesis (Ph.D.)-- Wichita State University, College of Liberal Arts and Sciences, Dept. of Mathematics, Statistics, and Physics"]},{"key":"dc:description.abstract","label":"Abstract","values":["It is well known that every smooth surface S is at least locally generated by the Dirac equation with real potential. In this dissertation, we study the inverse problem of recovering this potential and surface based on given Gaussian curvature and discrete Cauchy data on $z_n$ assuming that S is a Willmore surface $r : \\mathbb{D} \\rightarrow R^3$ We reduce this problem to several problems of the type: $|\\partial \\bar{u}|\\leq a|u|,$ $\\forall{z}\\in\\mathbb{D},$ $n = 1,2,3$ with given discrete Cauchy data on {$z_n$} For sequence $z_n$ we assume Blaschke condition $\\displaystyle\\sum\\limits_{n=1}^{\\infty}(1|-|z_n|)=\\infty$ Our main tool is Carleman estimates."]},{"key":"dc:title","label":"Title","values":["Continuation from discrete sets and inverse problems"]}]}],"canonical_facts":{"dc:contributor.advisor":["Bukhgeym, Alexander L."],"dc:creator":["Domme, Cristina Camelia"],"dc:date.accessioned":["2023-08-29T18:43:50Z"],"dc:date.available":["2023-08-29T18:43:50Z"],"dc:date.issued":["2023-07"],"dc:description":["Thesis (Ph.D.)-- Wichita State University, College of Liberal Arts and Sciences, Dept. of Mathematics, Statistics, and Physics"],"dc:description.abstract":["It is well known that every smooth surface S is at least locally generated by the Dirac equation with real potential. In this dissertation, we study the inverse problem of recovering this potential and surface based on given Gaussian curvature and discrete Cauchy data on $z_n$ assuming that S is a Willmore surface $r : \\mathbb{D} \\rightarrow R^3$ We reduce this problem to several problems of the type: $|\\partial \\bar{u}|\\leq a|u|,$ $\\forall{z}\\in\\mathbb{D},$ $n = 1,2,3$ with given discrete Cauchy data on {$z_n$} For sequence $z_n$ we assume Blaschke condition $\\displaystyle\\sum\\limits_{n=1}^{\\infty}(1|-|z_n|)=\\infty$ Our main tool is Carleman estimates."],"dc:identifier.other":["d23020s"],"dc:identifier.uri":["https://soar.wichita.edu/handle/10057/25700"],"dc:language.iso":["en_US"],"dc:publisher":["Wichita State University"],"dc:rights":["© Copyright 2023 by Cristina C. Domme All Rights Reserved"],"dc:title":["Continuation from discrete sets and inverse problems"],"dc:type":["Dissertation"]},"updated_at":"2026-08-21T16:50:43Z"}