Inequalities between Dirichlet and Neumann eigenvalues of the magnetic Laplacian

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F25%3A00616494" target="_blank" >RIV/61389005:_____/25:00616494 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007/s11005-025-01901-8" target="_blank" >https://link.springer.com/article/10.1007/s11005-025-01901-8</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11005-025-01901-8" target="_blank" >10.1007/s11005-025-01901-8</a>

Result language
angličtina
Original language name
Inequalities between Dirichlet and Neumann eigenvalues of the magnetic Laplacian
Original language description
We consider the magnetic Laplacian with the homogeneous magnetic field in two and three dimensions. We prove that the (k + 1)-th magnetic Neumann eigenvalue of a bounded convex planar domain is not larger than its k-th magnetic Dirichlet eigenvalue for all k ∈ N. In three dimensions, we restrict our attention to convex domains, which are invariant under rotation by an angle of π around an axis parallel to the magnetic field. For such domains, we prove that the (k + 2)-th magnetic Neumann eigenvalue is not larger than the k-th magnetic Dirichlet eigenvalue provided that this Dirichlet eigenvalue is simple. The proofs rely on a modification of the strategy suggested by Payne and developed further by Levine and Weinberger.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics

Project
<a href="/en/project/GA21-07129S" target="_blank" >GA21-07129S: New Effects from Time-Reversal Non-Invariance</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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