Green functions and the Dirichlet spectrum
comunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
comunitat-uji-handle4:
INVESTIGACIONMetadatos
Título
Green functions and the Dirichlet spectrumFecha de publicación
2020Editor
European Mathematical SocietyISSN
0213-2230Cita bibliográfica
BESSA, G. Pacelli; GIMENO, Vicent; JORGE, Luquesio. Green functions and the Dirichlet spectrum. Revista Matemática Iberoamericana, 2019, vol. 36, núm. 1, p. 1-36Tipo de documento
info:eu-repo/semantics/articleVersión de la editorial
https://www.ems-ph.org/journals/show_abstract.php?issn=0213-2230&vol=36&iss=1&rank=1Versión
info:eu-repo/semantics/acceptedVersionPalabras clave / Materias
Resumen
This article has results of four types. We show that the firsteigenvalueλ1(Ω) of the weighted Laplacian of a bounded domain withsmooth boundary can be obtained by S. Sato’s iteration scheme of ... [+]
This article has results of four types. We show that the firsteigenvalueλ1(Ω) of the weighted Laplacian of a bounded domain withsmooth boundary can be obtained by S. Sato’s iteration scheme of theGreen operator, taking the limitλ1(Ω) = limk→∞‖Gk(f)‖L2/‖Gk+1(f)‖L2for anyf∈L2(Ω,μ),f >0, (Theorems 2.1 & 2.2). Then, we study theL1(Ω,μ)-moment spectrum of Ω in terms of iterates of the Green oper-atorG, (Theorem 3.2), extendind the work of MacDonald-Meyers [29]to the weighted setting. As corollary, we obtain the first eigenvalue ofa weighted bounded domain in terms of theL1(Ω,μ)-moment spectrum,generalizing the work of Hurtado-Markvorsen-Palmer [25]. Finally, westudy the radial spectrumσrad(Bh(o,r)) of rotationally invariant geodesicballsBh(o,r) of model manifolds. In Theorems 5.4 & 5.6, we prove anidentity relating the radial eigenvalues ofσrad(Bh(o,r)) to an isoperimet-ric quotient, i.e.∑1/λradi=∫V(s)/S(s)ds,V(s) = vol(Bh(o,s)) andS(s) = vol(∂Bh(o,s)). We then consider a proper minimal surfaceM⊂R3and the extrinsic ball Ω =M∩BR3(o,r). We obtain upper and lower es-timates for the series∑λ−2i(Ω) in terms of the volume vol(Ω) and theradiusrof the extrinsic ball Ω, (Theorem 6.1). [-]
Publicado en
Revista Matemática Iberoamericana, 2019, vol. 36, núm. 1, p. 1-36Entidad financiadora
Universitat Jaume I | Brazilian National Research and Development Council (CNPq) | FUNCAP | Ministerio de Asunto Económicos y Transformación Digital
Código del proyecto o subvención
301581/2013-4 | 445993/2014-6 | UJI-B2016-07 | MTM2013-48371-C2-2-P
Derechos de acceso
© European Mathematical Society
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info:eu-repo/semantics/openAccess
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