The Bourgain Spaces and Recovery of Magnetic and Electric Potentials of Schrödinger Operators

Author

Yaowei Zhang, University of KentuckyFollow

Date Available

7-30-2016

Year of Publication

2016

Degree Name

Doctor of Philosophy (PhD)

Document Type

Doctoral Dissertation

College

Arts and Sciences

Department/School/Program

Mathematics

First Advisor

Dr. Russell Brown

Abstract

We consider the inverse problem for the magnetic Schrödinger operator with the assumption that the magnetic potential is in C^λ and the electric potential is of the form p₁ + div p₂ with p₁, p₂ ∈ C^λ. We use semiclassical pseudodifferential operators on semiclassical Sobolev spaces and Bourgain type spaces. The Bourgain type spaces are defined using the symbol of the operator h²Δ + hμ ⋅ D. Our main result gives a procedure for recovering the curl of the magnetic field and the electric potential from the Dirichlet to Neumann map. Our results are in dimension three and higher.

Digital Object Identifier (DOI)

http://dx.doi.org/10.13023/ETD.2016.353

Recommended Citation

Zhang, Yaowei, "The Bourgain Spaces and Recovery of Magnetic and Electric Potentials of Schrödinger Operators" (2016). Theses and Dissertations--Mathematics. 41.
https://uknowledge.uky.edu/math_etds/41