{"id":{"repo_id":"wichita-thes","oai_identifier":"oai:soar.wichita.edu:10057/25700"},"canonical_url":"https://search.dev.ndltd.org/etd/wichita-thes/oai:soar.wichita.edu: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":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2023,"date_issued":"2023-07","date_published":"2023-07","updated_at":"2026-07-24T06:05:25Z","subjects":[],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["hdl:10057/25700"],"render_values":[{"text":"hdl:10057/25700","href":null,"code":true}]}]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2023-07"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["hdl:10057/25700"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.other","label":"Dc Description Other","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:date.issued":["2023-07"],"dc:description.other":["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":["hdl:10057/25700"],"dc:title":["Continuation from discrete sets and inverse problems"],"dc:type":["Dissertation"]},"updated_at":"2026-07-24T06:05:25Z"}