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In this paper we study inverse boundary value problems with partial data forthe magnetic Schr\"odinger operator. In the case of an infinite slab in $R^n$,$n\ge 3$, we establish that the magnetic field and the electric potential canbe determined uniquely, when the Dirichlet and Neumann data are given either onthe different boundary hyperplanes of the slab or on the same hyperplane. Thisis a generalization of the results of [41], obtained for the Schr\"odingeroperator without magnetic potentials. In the case of a bounded domain in $R^n$,$n\ge 3$, extending the results of [2], we show the unique determination of themagnetic field and electric potential from the Dirichlet and Neumann data,given on two arbitrary open subsets of the boundary, provided that the magneticand electric potentials are known in a neighborhood of the boundary.Generalizing the results of [31], we also obtain uniqueness results for themagnetic Schr\"odinger operator, when the Dirichlet and Neumann data are knownon the same part of the boundary, assuming that the inaccessible part of theboundary is a part of a hyperplane.

Inverse problems with partial data for a magnetic Schr\"odinger operator in an infinite slab and on a bounded domain