On the Lp norm of the torsion function

M. van den Berg; T. Kappeler

doi:10.1007/s11587-018-0412-x

On the L^p norm of the torsion function

M. van den Berg^*, T. Kappeler

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

192 Downloads (Pure)

Abstract

Bounds are obtained for the Lp norm of the torsion function vΩ, i.e. the solution of −Δv=1,v∈H10(Ω), in terms of the Lebesgue measure of Ω and the principal eigenvalue λ1(Ω) of the Dirichlet Laplacian acting in L2(Ω). We show that these bounds are sharp for 1≤p≤2.

Original language	English
Pages (from-to)	399-414
Number of pages	16
Journal	Ricerche di Matematica
Volume	68
Early online date	29 Jun 2018
DOIs	https://doi.org/10.1007/s11587-018-0412-x
Publication status	E-pub ahead of print - 29 Jun 2018

Keywords

$$L^p$$Lpnorm
Dirichlet conditions
Finite Lebesgue measure
Torsion function

Access to Document

10.1007/s11587-018-0412-x

Full-text PDF (accepted author manuscript)
This is the author accepted manuscript (AAM). The final published version (version of record) is available online via Springer Verlag at https://link.springer.com/article/10.1007%2Fs11587-018-0412-x . Please refer to any applicable terms of use of the publisher.
Accepted author manuscript, 305 KB

Handle.net

Persistent link

Cite this

@article{37e3ac7d179a4b9fa0ea60eade326700,

title = "On the Lp norm of the torsion function",

abstract = "Bounds are obtained for the Lp norm of the torsion function vΩ, i.e. the solution of −Δv=1,v∈H10(Ω), in terms of the Lebesgue measure of Ω and the principal eigenvalue λ1(Ω) of the Dirichlet Laplacian acting in L2(Ω). We show that these bounds are sharp for 1≤p≤2. ",

keywords = "\$\$L\textasciicircum{}p\$\$Lpnorm, Dirichlet conditions, Finite Lebesgue measure, Torsion function",

author = "\{van den Berg\}, M. and T. Kappeler",

year = "2018",

month = jun,

day = "29",

doi = "10.1007/s11587-018-0412-x",

language = "English",

volume = "68",

pages = "399--414",

journal = "Ricerche di Matematica",

issn = "0035-5038",

publisher = "Springer Milan",

}

TY - JOUR

T1 - On the Lp norm of the torsion function

AU - van den Berg, M.

AU - Kappeler, T.

PY - 2018/6/29

Y1 - 2018/6/29

N2 - Bounds are obtained for the Lp norm of the torsion function vΩ, i.e. the solution of −Δv=1,v∈H10(Ω), in terms of the Lebesgue measure of Ω and the principal eigenvalue λ1(Ω) of the Dirichlet Laplacian acting in L2(Ω). We show that these bounds are sharp for 1≤p≤2.

AB - Bounds are obtained for the Lp norm of the torsion function vΩ, i.e. the solution of −Δv=1,v∈H10(Ω), in terms of the Lebesgue measure of Ω and the principal eigenvalue λ1(Ω) of the Dirichlet Laplacian acting in L2(Ω). We show that these bounds are sharp for 1≤p≤2.

KW - $$L^p$$Lpnorm

KW - Dirichlet conditions

KW - Finite Lebesgue measure

KW - Torsion function

UR - https://www.scopus.com/pages/publications/85049123120

U2 - 10.1007/s11587-018-0412-x

DO - 10.1007/s11587-018-0412-x

M3 - Article (Academic Journal)

AN - SCOPUS:85049123120

SN - 0035-5038

VL - 68

SP - 399

EP - 414

JO - Ricerche di Matematica

JF - Ricerche di Matematica

ER -