A Variational Formulation for Dirac Operators in Bounded Domains. Applications to Spectral Geometric Inequalities

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F21%3A00544712" target="_blank" >RIV/61389005:_____/21:00544712 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s00220-021-03959-6" target="_blank" >https://doi.org/10.1007/s00220-021-03959-6</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00220-021-03959-6" target="_blank" >10.1007/s00220-021-03959-6</a>

Result language
angličtina
Original language name
A Variational Formulation for Dirac Operators in Bounded Domains. Applications to Spectral Geometric Inequalities
Original language description
We investigate spectral features of the Dirac operator with infinite mass boundary conditions in a smooth bounded domain of R-2. Motivated by spectral geometric inequalities, we prove a non-linear variational formulation to characterize its principal eigenvalue. This characterization turns out to be very robust and allows for a simple proof of a Szego type inequality as well as a new reformulation of a Faber-Krahn type inequality for this operator. The paper is complemented with strong numerical evidences supporting the existence of a Faber-Krahn type inequality.
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
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OECD FORD branch
10301 - Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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