Simultaneous reconstruction of two potentials for a nonconservative Schrödinger equation with dynamic boundary conditions

2025/02/04 by Carrllo, Hugo, Mercado, Alberto, Morales, Roberto
#Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2502.02758

Abstract

In this article, we consider an inverse problem involving the simultaneous reconstruction of two real valued potentials for a Schrödinger 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.

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