A sharp upper bound for the first dirichlet eigenvalue and the growth of the isoperimetric constant of convex domains

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F08%3A00311170" target="_blank" >RIV/61389005:_____/08:00311170 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
A sharp upper bound for the first dirichlet eigenvalue and the growth of the isoperimetric constant of convex domains
Original language description
We show that as the ratio between the first Dirichlet eigenvalues of a convex domain and of the ball with the same volume becomes large, the same must happen to the corresponding ratio of isoperimetric constants. The proof is based on the generalizationto arbitrary dimensions of Polya and Szego's 1951 upper bound for the first eigenvalue of the Dirichlet Laplacian on planar star-shaped domains which depends on the support function of the domain.
Czech name
Optimalni horni odhad na prvni dirichletovskou vlastni hodnotu
Czech description
Ukazujeme, ze kdyz se pomer prvnich dirichletovskych vlastnich hodnot konvexni oblasti a koule stejneho objemu stane velkym, velky musi byt i odpovidajici pomer isoperimetrickych konstant. Dukaz je zalozen na zobecneni do libovolne dimense odhadu, odvozenem v roce 1951 pany Polya a Szego, na prvni dirichletovskou vlastni hodnotu hvezdicovitych oblastí.

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/LC06002" target="_blank" >LC06002: Doppler Institute for Mathematical Physics and Applied Mathematics</a><br>
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2008
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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