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SEMICLASSICAL ASYMPTOTICS OF THE GROUND STATE ENERGY FOR THE NEUMANN PROBLEM ASSOCIATED WITH SUPERCONDUCTIVITY

Junichi Aramaki

Abstract


We consider  the Neumann-Schr\"odinger operator in a bounded domain in $\rr ^2$. In the case, where the corresponding magnetic field is non-constant, we shall get the semiclassical asymptotics with lower order term of the first eigenvalue. This paper is an improvement of results of Helffer and Morame [8] in which they got the asymptotics for the constant magnetic field case.

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