Some stability inequalities for hybrid inverse problems

TL;DR

This paper investigates stability inequalities for hybrid inverse problems involving Schrödinger and Helmholtz equations, focusing on determining coefficients from internal energy measurements, and establishes both Lipschitz and H"older stability results.

Contribution

It introduces new stability inequalities for hybrid inverse problems, providing theoretical guarantees for coefficient recovery from internal energy data.

Findings

Established local Lipschitz stability inequalities.

Proved conditional H"older stability inequalities.

Applied to inverse problems for Schrödinger and Helmholtz equations.

Abstract

We study some hybrid inverse problems associated to BVP's for Schr\"odinger and Helmholtz type equations. The inverse problems we consider consist in the determination of coefficients from the knowledge of internal energies. We establish local Lipschitz stability inequalities as well as conditional H\"older stability inequalities.