Scattering problems for perturbations of the multidimensional biharmonic operator
|Author:||Tyni, Teemu1; Serov, Valery1|
1Department of Mathematical Sciences, FI-90014 University of Oulu, Finland
|Online Access:||PDF Full Text (PDF, 0.4 MB)|
|Persistent link:|| http://urn.fi/urn:nbn:fi-fe2019040411052
American Institute of Mathematical Sciences,
|Publish Date:|| 2019-04-04
Some scattering problems for the multidimensional biharmonic operator are studied. The operator is perturbed by first and zero order perturbations, which maybe complex-valued and singular. We show that the solutions to direct scattering problem satisfy a Lippmann-Schwinger equation, and that this integral equation has a unique solution in the weighted Sobolev space H2−δ. The main result of this paper is the proof of Saito's formula, which can be used to prove a uniqueness theorem for the inverse scattering problem. The proof of Saito's formula is based on norm estimates for the resolvent of the direct operator in H1−δ.
Inverse problems and imaging
|Pages:||205 - 227|
|Type of Publication:||
A1 Journal article – refereed
|Field of Science:||
This work was supported by the Academy of Finland (application number 250215, Finnish Programme for Centres of Excellence in Research 2012–2017). The first author was supported by the Doctoral Programme of Exact Sciences at the University of Oulu, Finland.
Inverse Problems & Imaging © 2018 Published by AIMS. All rights reserved.