# H\"older stably determining the time-dependent electromagnetic potential of the Schr\"odinger equation

## TL;DR

This paper proves that the time- and space-dependent electromagnetic potential in the Schr"odinger equation can be stably reconstructed from boundary data, with H"older stability, improving upon typical logarithmic stability estimates.

## Contribution

The paper establishes H"older stability estimates for the inverse problem of determining electromagnetic potentials in the Schr"odinger equation from boundary observations.

## Key findings

- H"older stability estimates for electric and magnetic potentials
- Unique determination of potentials from boundary data
- Improved stability compared to logarithmic estimates

## Abstract

We consider the inverse problem of determining the time and space dependent electromagnetic potential of the Schr\"odinger equation in a bounded domain of $\mathbb R^n$, $n\geq 2$, by boundary observation of the solution over the entire time span. Assuming that the divergence of the magnetic potential is fixed, we prove that the electric potential and the magnetic potential can be H\"older stably retrieved from these data, whereas stability estimates for inverse time-dependent coefficients problems of evolution partial differential equations are usually of logarithmic type.