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.

Author

• Domme, Cristina Camelia

Identifier

hdl:10057/25700

OAI identifier oai:identifier

oai:soar.wichita.edu:10057/25700