# H\"older Stable Recovery of Time-Dependent Electromagnetic Potentials Appearing in a Dynamical Anisotropic Schr\"odinger Equation

## TL;DR

This paper establishes a H"older stability result for recovering time- and space-dependent electromagnetic potentials in a Schr"odinger equation on a Riemannian manifold, removing previous smallness constraints.

## Contribution

It proves H"older stability for the inverse problem of determining electromagnetic potentials, extending prior work by removing the smallness assumption on the magnetic potential.

## Key findings

- H"older stability of potential recovery from Dirichlet-to-Neumann data
- Recovery of electric and magnetic potentials without smallness constraints
- Extension to general Riemannian manifolds with boundary

## Abstract

We consider the inverse problem of H\"oldder-stably determining the time- and space-dependent coefficients of the Schr\"odinger equation on a simple Riemannian manifold with boundary of dimension $n\geq2$ from knowledge of the Dirichlet-to-Neumann map. Assuming the divergence of the magnetic potential is known, we show that the electric and magnetic potentials can be H\"older-stably recovered from these data. Here we also remove the smallness assumption for the solenoidal part of the magnetic potential present in previous results.