Continuation from discrete sets and inverse problems

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 R³ 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.

Grantor dc:publisher

Wichita State University

Year dc:date.issued

2023

Author dc:creator

• Domme, Cristina Camelia

Advisor dc:contributor.advisor

• Bukhgeym, Alexander L.

Statement dc:rights

• © Copyright 2023 by Cristina C. Domme All Rights Reserved

Language dc:language.iso

en_US

Dc Identifier Other

d23020s

OAI record oai:identifier

https://soar.wichita.edu/oai/request?verb=GetRecord&metadataPrefix=dim&identifier=oai%3Anull%3A10057%2F25700