Improved inequalities between Dirichlet and Neumann eigenvalues of the biharmonic operator

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F24%3A00585813" target="_blank" >RIV/61389005:_____/24:00585813 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1090/proc/16749" target="_blank" >https://doi.org/10.1090/proc/16749</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1090/proc/16749" target="_blank" >10.1090/proc/16749</a>

Result language
angličtina
Original language name
Improved inequalities between Dirichlet and Neumann eigenvalues of the biharmonic operator
Original language description
We prove that the (k + d)-th Neumann eigenvalue of the biharmonic operator on a bounded connected d -dimensional (d >= 2) Lipschitz domain is not larger than its k-th Dirichlet eigenvalue for all k is an element of N. For a special class of domains with symmetries we obtain a stronger inequality. Namely, for this class of domains, we prove that the (k + d + 1)-th Neumann eigenvalue of the biharmonic operator does not exceed its k-th Dirichlet eigenvalue for all k is an element of N. In particular, in two dimensions, this special class consists of domains having an axis of symmetry.
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
10101 - Pure 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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