Simultaneous reconstruction of two potentials for a nonconservative Schr\"odinger equation with dynamic boundary conditions
Analysis of PDEs
2025-02-06 v1 Optimization and Control
Abstract
In this article, we consider an inverse problem involving the simultaneous reconstruction of two real valued potentials for a Schr\"odinger equation with mixed boundary conditions: a dynamic boundary condition of Wentzell type and a Dirichler boundary condition. The main result of this paper is a Lipschitz stability estimate for such potentials from a single measurement of the flux. This result is deduced using the Bukhgeim-Klibanov method and a suitable Carleman estimate where the weight function depends on Minkowski's functional.
Keywords
Cite
@article{arxiv.2502.02758,
title = {Simultaneous reconstruction of two potentials for a nonconservative Schr\"odinger equation with dynamic boundary conditions},
author = {Hugo Carrllo and Alberto Mercado and Roberto Morales},
journal= {arXiv preprint arXiv:2502.02758},
year = {2025}
}