Year: 2026
Type: preprint
Abstract: We prove that the Dirichlet-to-Neumann map associated to the Schrödinger operator $-Δ+q$ on a planar bounded Lipschitz domain uniquely determines an arbitrary complex-valued potential $q\in L^p$, $p>1$, whenever zero is not a Dirichlet eigenvalue. Our argument uses Nachman's d-bar equation only at sufficiently large complex frequencies, where exceptional points are absent. A new annular frequency estimate converts the first asymptotic coefficient of the complex geometric optics solutions into a pointwise bound for a primitive of the potential difference, reducing the inverse problem to a unique-continuation argument.
Source: arXiv (Cornell University)
Author: Feizmohammadi, Ali
Institution: University of Toronto
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214232852