Partial data inverse problems for magnetic Schr\"odinger operators with potentials of low regularity

TL;DR

This paper proves a unique determination of magnetic and electric potentials with low regularity from partial boundary data in inverse boundary problems, extending previous results to less smooth potentials.

Contribution

It extends the uniqueness results for inverse boundary problems to magnetic potentials in $W^{1,n} \,\cap\, L^\infty$ and electric potentials in $L^n$, with partial data.

Findings

Global uniqueness for magnetic Schrödinger operator with low regularity potentials

Extension of previous results to less smooth potentials

Application to inverse boundary problems for advection-diffusion operator

Abstract

We establish a global uniqueness result for an inverse boundary problem with partial data for the magnetic Schr\"odinger operator with a magnetic potential of class $W^{1,n}\cap L^\infty$, and an electric potential of class $L^n$. Our result is an extension, in terms of the regularity of the potentials, of the results [16] and [25]. As a consequence, we also show global uniqueness for a partial data inverse boundary problem for the advection-diffusion operator with the advection term of class $W^{1,n}\cap L^\infty$.