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

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About: A sharp upper bound for the first dirichlet eigenvalue and the growth of the isoperimetric constant of convex domains Goto Sponge NotDistinct Permalink

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
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 generalization to 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. 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 generalization to 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. (en) 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. (cs)
Title	A sharp upper bound for the first dirichlet eigenvalue and the growth of the isoperimetric constant of convex domains A sharp upper bound for the first dirichlet eigenvalue and the growth of the isoperimetric constant of convex domains (en) Optimalni horni odhad na prvni dirichletovskou vlastni hodnotu (cs)
skos:prefLabel	A sharp upper bound for the first dirichlet eigenvalue and the growth of the isoperimetric constant of convex domains A sharp upper bound for the first dirichlet eigenvalue and the growth of the isoperimetric constant of convex domains (en) Optimalni horni odhad na prvni dirichletovskou vlastni hodnotu (cs)
skos:notation	RIV/61389005:_____/08:00311170!RIV09-AV0-61389005
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(LC06002), Z(AV0Z10480505)
http://linked.open...iv/cisloPeriodika	8
http://linked.open...vai/riv/dodaniDat	2009
http://linked.open...aciTvurceVysledku	Krejčiřík, David
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Ústav jaderné fyziky AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	354495
http://linked.open...ai/riv/idVysledku	RIV/61389005:_____/08:00311170
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	FUNDAMENTAL-FREQUENCY (en)
http://linked.open.../riv/klicoveSlovo	FUNDAMENTAL-FREQUENCY
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[FD9B37ABE6DE]
http://linked.open...i/riv/nazevZdroje	Proceedings of the American Mathematical Society
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Doppler Institute for Mathematical Physics and Applied Mathematics
http://linked.open...UplatneniVysledku	2008
http://linked.open...v/svazekPeriodika	136
http://linked.open...iv/tvurceVysledku	Krejčiřík, David Freitas, P.
http://linked.open...ain/vavai/riv/wos	000256156100044
http://linked.open...n/vavai/riv/zamer	Jaderná fyzika a příbuzné obory v základním, aplikovaném a interdisciplinárním výzkumu
issn	0002-9939
number of pages	10 (xsd:int)
is http://linked.open...avai/riv/vysledek of	A sharp upper bound for the first dirichlet eigenvalue and the growth of the isoperimetric constant of convex domains A sharp upper bound for the first dirichlet eigenvalue and the growth of the isoperimetric constant of convex domains A sharp upper bound for the first dirichlet eigenvalue and the growth of the isoperimetric constant of convex domains A sharp upper bound for the first dirichlet eigenvalue and the growth of the isoperimetric constant of convex domains

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