Let be a smooth, non-closed, simple curve whose image is symmetric with respect to the y-axis, and let D be a planar domain consisting of the points on one side of within a suitable distance ı of . Denote by odd 1 .D/ the smallest nontrivial Neumann eigenvalue having a corresponding eigenfunction that is odd with respect to the y-axis. If satisfies some simple geometric conditions, then odd 1 .D/ can be sharply estimated from below in terms of the length of , its curvature, and ı. Moreover, we give explicit conditions on ı that ensure odd 1 .D/ D 1 .D/. Finally, we can extend our bound on odd 1 .D/ to a certain class of three-dimensional domains. In both the two- and three-dimensional settings, our domains are generically non-convex

Brandolini B., Chiacchio F., Dryden E.B., & Langford J.J. (2018). Sharp Poincaré inequalities in a class of non-convex sets. JOURNAL OF SPECTRAL THEORY, 8(4), 1583-1615 [10.4171/JST/236].

Sharp Poincaré inequalities in a class of non-convex sets

Brandolini B.
;
2018

Abstract

Let be a smooth, non-closed, simple curve whose image is symmetric with respect to the y-axis, and let D be a planar domain consisting of the points on one side of within a suitable distance ı of . Denote by odd 1 .D/ the smallest nontrivial Neumann eigenvalue having a corresponding eigenfunction that is odd with respect to the y-axis. If satisfies some simple geometric conditions, then odd 1 .D/ can be sharply estimated from below in terms of the length of , its curvature, and ı. Moreover, we give explicit conditions on ı that ensure odd 1 .D/ D 1 .D/. Finally, we can extend our bound on odd 1 .D/ to a certain class of three-dimensional domains. In both the two- and three-dimensional settings, our domains are generically non-convex
Settore MAT/05 - Analisi Matematica
Brandolini B., Chiacchio F., Dryden E.B., & Langford J.J. (2018). Sharp Poincaré inequalities in a class of non-convex sets. JOURNAL OF SPECTRAL THEORY, 8(4), 1583-1615 [10.4171/JST/236].
File in questo prodotto:
File Dimensione Formato  
JST(2018).pdf

accesso aperto

Tipologia: Versione Editoriale
Dimensione 805.65 kB
Formato Adobe PDF
805.65 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10447/493959
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 7
  • ???jsp.display-item.citation.isi??? 7
social impact