A geometric bound on the lowest magnetic Neumann eigenvalue via the torsion function

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F24%3A00598966" target="_blank" >RIV/61389005:_____/24:00598966 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1137/23M1624658" target="_blank" >https://doi.org/10.1137/23M1624658</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/23M1624658" target="_blank" >10.1137/23M1624658</a>

Result language
angličtina
Original language name
A geometric bound on the lowest magnetic Neumann eigenvalue via the torsion function
Original language description
We obtain an upper bound on the lowest magnetic Neumann eigenvalue of a bounded, convex, smooth, planar domain with moderate intensity of the homogeneous magnetic field. This bound is given as a product of a purely geometric factor expressed in terms of the torsion function and of the lowest magnetic Neumann eigenvalue of the disk having the same maximal value of the torsion function as the domain. The bound is sharp in the sense that equality is attained for disks. Furthermore, we derive from our upper bound that the lowest magnetic Neumann eigenvalue with the homogeneous magnetic field is maximized by the disk among all ellipses of fixed area provided that the intensity of the magnetic field does not exceed an explicit constant dependent only on the fixed area.
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
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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