On principal frequencies, volume and inradius in convex sets

Lorenzo Brasco; Dario Cesare Severo Mazzoleni

doi:10.1007/s00030-019-0614-2

On principal frequencies, volume and inradius in convex sets

Lorenzo Brasco
, Dario Cesare Severo Mazzoleni^*

^*Autore corrispondente per questo lavoro

Università Cattolica del Sacro Cuore

University of Ferrara

Risultato della ricerca: Contributo in rivista › Articolo › peer review

Abstract

We provide a sharp double-sided estimate for Poincaré–Sobolev constants on a convex set, in terms of its inradius and N- dimensional measure. Our results extend and unify previous works by Hersch and Protter (for the first eigenvalue) and of Makai, Pólya and Szegő (for the torsional rigidity), by means of a single proof.

Lingua originale	Inglese
pagine (da-a)	1-26
Numero di pagine	26
Rivista	NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS
Volume	27
DOI	https://doi.org/10.1007/s00030-019-0614-2
Stato di pubblicazione	Pubblicato - 2020

Keywords

Convex sets
Inradius
Nonlinear eigenvalue problems
Torsional rigidity

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10.1007/s00030-019-0614-2

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title = "On principal frequencies, volume and inradius in convex sets",

abstract = "We provide a sharp double-sided estimate for Poincar{\'e}–Sobolev constants on a convex set, in terms of its inradius and N- dimensional measure. Our results extend and unify previous works by Hersch and Protter (for the first eigenvalue) and of Makai, P{\'o}lya and Szeg{\H o} (for the torsional rigidity), by means of a single proof.",

keywords = "Convex sets, Inradius, Nonlinear eigenvalue problems, Torsional rigidity, Convex sets, Inradius, Nonlinear eigenvalue problems, Torsional rigidity",

author = "Lorenzo Brasco and Mazzoleni, \{Dario Cesare Severo\}",

year = "2020",

doi = "10.1007/s00030-019-0614-2",

language = "English",

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pages = "1--26",

journal = "NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS",

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TY - JOUR

T1 - On principal frequencies, volume and inradius in convex sets

AU - Brasco, Lorenzo

AU - Mazzoleni, Dario Cesare Severo

PY - 2020

Y1 - 2020

N2 - We provide a sharp double-sided estimate for Poincaré–Sobolev constants on a convex set, in terms of its inradius and N- dimensional measure. Our results extend and unify previous works by Hersch and Protter (for the first eigenvalue) and of Makai, Pólya and Szegő (for the torsional rigidity), by means of a single proof.

AB - We provide a sharp double-sided estimate for Poincaré–Sobolev constants on a convex set, in terms of its inradius and N- dimensional measure. Our results extend and unify previous works by Hersch and Protter (for the first eigenvalue) and of Makai, Pólya and Szegő (for the torsional rigidity), by means of a single proof.

KW - Convex sets

KW - Inradius

KW - Nonlinear eigenvalue problems

KW - Torsional rigidity

KW - Convex sets

KW - Inradius

KW - Nonlinear eigenvalue problems

KW - Torsional rigidity

UR - http://hdl.handle.net/10807/145703

UR - https://link.springer.com/article/10.1007/s00030-019-0614-2

U2 - 10.1007/s00030-019-0614-2

DO - 10.1007/s00030-019-0614-2

M3 - Article

SN - 1021-9722

VL - 27

SP - 1

EP - 26

JO - NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS

JF - NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS

ER -

On principal frequencies, volume and inradius in convex sets

Abstract

Keywords

Accesso al documento

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