Partial data inverse problems for magnetic Schrödinger operators with potentials of low regularity

We establish a global uniqueness result for an inverse boundary problem with partial data for the magnetic Schrödinger operator with a magnetic potential of class $W^{1,n}\cap L^{\mathrm{\infty }}$, 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 $W^{1,n}\cap L^{\mathrm{\infty }}$.