We compute the sum and number of eigenvalues for a certain class of magnetic Schrödinger operators in a domain with boundary. Functions in the domain of the operator satisfy a (magnetic) Robin condition. The calculations are valid in the semi-classical asymptotic limit and the eigenvalues concerned correspond to eigenstates localized near the boundary of the domain. The formulas we derive display the influence of the boundary and the boundary condition and are valid under a weak regularity assumption of the boundary function. Our approach relies on three main points: reduction to the boundary, construction of boundary coherent states, and handling the boundary term as a surface electric potential and controlling the errors by various Lieb-Thirring inequalities.
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