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Stability of gaps for periodic potentials under variation of a magnetic field. (English) Zbl 0586.35084
Let $$H_ 0(B)$$ denote the Hamiltonian of a free electron in a magnetic field B. Let V be a periodic potential. We show that if an interval [a,b] is not in the spectrum of $$H_ 0(B_ 0)+V$$ for some $$B_ 0$$, then it is not in the spectrum for all B sufficiently close to $$B_ 0$$.

##### MSC:
 35Q99 Partial differential equations of mathematical physics and other areas of application 35B10 Periodic solutions to PDEs 35P15 Estimates of eigenvalues in context of PDEs 35B37 PDE in connection with control problems (MSC2000)
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