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

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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

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10.1007/s11587-018-0412-x

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Cite this

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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. ",

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AU - van den Berg, M.

AU - Kappeler, T.

PY - 2018/6/29

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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

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