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Continuation from discrete sets and inverse problems
Domme, Cristina Camelia
Domme, Cristina Camelia
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2023-07
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Dissertation
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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.
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Thesis (Ph.D.)-- Wichita State University, College of Liberal Arts and Sciences, Dept. of Mathematics, Statistics, and Physics
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Wichita State University
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© Copyright 2023 by Cristina C. Domme
All Rights Reserved