5.12.2020 Uniqueness results for fractional Calderón problems (Covi)
The dissertation of Giovanni Covi studies the fractional Schrödinger equation, which appears in the study of anomalous diffusion and serves as a generalization of models currently used in the fields of medical and industrial imaging. The dissertation considers numerous perturbed versions of such equation and establishes uniqueness and recoverability results.
“The central objective of the field of Inverse problems consists in determining the properties of the interior of an object by studying its exterior, or its surface”, says Covi.
“This kind of problems is of central interest in many practical applications, including modern scanning techniques for medical imaging, mineral prospection, and even space exploration.”
One of the main results shows that any local perturbation of the fractional Schrödinger equation can be uniquely recovered from the corresponding Dirichlet to Neumann map, even in the higher order case. In particular, unique recoverability and reconstruction was shown to hold for the fractional conductivity equation and the magnetic Schrödinger equation. These results promise to have interesting applications in the study of nonlocal phenomena.
Another main result shows that the bundary and the bulk potentials can be simultaneously recovered from boundary data in the case of a local Calderon problem with mixed Robin conditions. The main application of this result arises in the problem of corrosion detection. This result is however also interesting from a theoretical point of view, as such problem is related to the fractional one via the Caffarelli-Silvestre extension.
The dissertation is published in JYU Dissertation series, number 318, University of Jyväskylä, Jyväskylä 2020.
ISBN 978-951-39-8391-8 (PDF) URN:ISBN:978-951-39-8391-8 ISSN 2489-9003
Link to the publication: http://urn.fi/URN:ISBN:978-951-39-8391-8
For further information
Giovanni Covi, giovanni.g.covi@jyu.fi
M.Sc. Giovanni Covi defends his doctoral dissertation in Mathematics "Uniqueness results for fractional Calderón problems" at the University of Jyväskylä in 5th of December 2021 at 12 noon. Opponent is University Lecturer Petri Ola from University of Helsinki and Custos is Professor Mikko Salo from University of Jyväskylä. The doctoral dissertation is held in English.
The audience can follow the dissertation online.
Link to the online event: https://r.jyu.fi/dissertation-covi-051220
Phone number to which the audience can present possible additional questions at the end of the event (to the custos):
