We analyze the 2D magnetic Laplacian in the semiclassical limit in the case when the magnetic field vanishes along a smooth curve. In particular, we prove local and micro-local estimates for the eigenfunctions and a complete asymptotic expansion of the eigenpairs in powers of .
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Nicolas Dombrowski, Nicolas Raymond, Semiclassical analysis with vanishing magnetic fields. J. Spectr. Theory 3 (2013), no. 3, pp. 423–464DOI 10.4171/JST/50