# Inverse scattering for the Laplace operator with boundary conditions on Lipschitz surfaces

@article{Mantile2019InverseSF,
title={Inverse scattering for the Laplace operator with boundary conditions on Lipschitz surfaces},
author={Andrea Mantile and Andrea Posilicano},
journal={Inverse Problems},
year={2019}
}
• Published 26 January 2019
• Mathematics
• Inverse Problems
We provide a general scheme, in the combined frameworks of Mathematical Scattering Theory and Factorization Method, for inverse scattering for the couple of self-adjoint operators $(\widetilde\Delta,\Delta)$, where $\Delta$ is the free Laplacian in $L^{2}({\mathbb R}^{3})$ and $\widetilde\Delta$ is one of its singular perturbations, i.e., such that the set $\{u\in H^{2}({\mathbb R}^{3})\cap \text{dom}(\widetilde\Delta)\, :\, \Delta u=\widetilde\Delta u\}$ is dense. Typically $\widetilde\Delta… 2 Citations Inverse wave scattering in the Laplace domain: A factorization method approach • Mathematics Proceedings of the American Mathematical Society • 2020 Let$\Delta_{\Lambda}\le \lambda_{\Lambda}\$ be a semi-bounded self-adjoint realization of the Laplace operator with boundary conditions (Dirichlet, Neumann, semi-transparent) assigned on the
Inverse wave scattering in the time domain for point scatterers
• Mathematics
• 2021
Abstract. Let ∆α,Y be the bounded from above self-adjoint realization in L (R) of the Laplacian with n point scatterers placed at Y = {y1, . . . , yn} ⊂ R, the parameters (α1, . . . αn) ≡ α ∈ R being