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

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