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In this article, we study stability estimates when recovering magnetic fieldsand electric potentials in a simply connected open subset in $R^n$ with $n \geq3$, from measurements on open subsets of its boundary. This inverse problem isassociated with a magnetic Schr\"odinger operator. Our estimates arequantitative versions of the uniqueness results obtained by D. Dos SantosFerreira, C. E. Kenig, J. Sj\"ostrand and G. Uhlmann in [13]. The moduli ofcontinuity are of logarithmic type.

Stability estimates for the magnetic Schr\"odinger operator with partial measurements