Abstract. In this paper we study local stability estimates for a magnetic Schrödinger operator with partial data on an open bounded set in dimension n ≥ 3. This is the corresponding stability estimates for the identifiability result obtained by Bukgheim and Uhlmann [2] in the presence of magnetic field and when the measurements for the DirichletNeumann map are taken on a neighborhood of the illuminated region of the boundary for functions supported on a neighborhood of the shadow region. We obtain log log-estimates for magnetic potential and log log log for electrical potential.

In this article, we study stability estimates when recovering magnetic fields and electric potentials in a simply connected open subset in R n with n ≥ 3, from measurements on open subsets of its boundary. This inverse problem is associated with a magnetic Schrödinger operator. Our estimates are quantitative versions of the uniqueness results obtained by D. Dos Santos Ferreira, C. E. Kenig, J. Sjöstrand and G. Uhlmann in [13]. The moduli of continuity are of logarithmic type. Contents 42 2 − σ 3(σ+1) holds for all χ Ω q j ∈ Q(Ω, M, σ) and for all χ Ω A j ∈ A (Ω, M, σ) satisfying A

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We study the inverse scattering problem of determining a magnetic field and electric potential from scattering measurements corresponding to finitely many plane waves. The main result shows that the coefficients are uniquely determined by 2n measurements up to a natural gauge. We also show that one can recover the full first-order term for a related equation having no gauge invariance, and that it is possible to reduce the number of measurements if the coefficients have certain symmetries. This work extends the fixed angle scattering results of Rakesh and Salo (SIAM J Math Anal 52(6):5467–5499, 2020) and (Inverse Probl 36(3):035005, 2020) to Hamiltonians with first-order perturbations, and it is based on wave equation methods and Carleman estimates.

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