Scattering problems for perturbations of the multidimensional biharmonic operator

Abstract

<div lang="en" class="abs"><p class="abs_header">Abstract</p><p>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 \(H_{-δ}^2\). 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 \(H_{-δ}^1\).</p></div>