# Inverse Problems for Ultrahyperbolic Schr\"odinger Equations

## TL;DR

This paper develops a Carleman estimate for ultrahyperbolic Schrödinger equations and proves Hölder stability for inverse problems involving coefficient or source term identification using boundary data.

## Contribution

It introduces a novel Carleman estimate and establishes stability results for inverse problems in ultrahyperbolic Schrödinger equations.

## Key findings

- Established a global Carleman estimate for the ultrahyperbolic Schrödinger equation.
- Proved Hölder stability for inverse coefficient and source term problems.
- Demonstrated the effectiveness of boundary data in solving inverse problems.

## Abstract

In this paper, we establish a global Carleman estimate for an Ultrahyperbolic Schr\"odinger equation. Moreover, we prove H\"older stability for the inverse problem of determining a coefficient or a source term in the Ultrahyperbolic Schr\"odinger equation by some lateral boundary data.

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Source: https://tomesphere.com/paper/1704.06780