Continuation from discrete sets and inverse problems

dc.contributor.advisorBukhgeym, Alexander L.
dc.contributor.authorDomme, Cristina Camelia
dc.date.accessioned2023-08-29T18:43:50Z
dc.date.available2023-08-29T18:43:50Z
dc.date.issued2023-07
dc.descriptionThesis (Ph.D.)-- Wichita State University, College of Liberal Arts and Sciences, Dept. of Mathematics, Statistics, and Physics
dc.description.abstractIt 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.format.extentvii, 44 pages
dc.identifier.otherd23020s
dc.identifier.urihttps://soar.wichita.edu/handle/10057/25700
dc.language.isoen_US
dc.publisherWichita State University
dc.rights© Copyright 2023 by Cristina C. Domme All Rights Reserved
dc.subject.lcshElectronic dissertation
dc.titleContinuation from discrete sets and inverse problems
dc.typeDissertation
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