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On the ${ L}^{ p}$ norm of the torsion function


Berg, M van den; Kappeler, Thomas (2019). On the ${ L}^{ p}$ norm of the torsion function. Ricerche di Matematica, 68(2):399-414.

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.

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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Additional indexing

Other titles:On the Lp norm of the torsion function
Item Type:Journal Article, not_refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Applied Mathematics, General Mathematics
Language:English
Date:1 December 2019
Deposited On:23 Jan 2019 12:48
Last Modified:09 Nov 2019 02:01
Publisher:Springer
ISSN:0035-5038
OA Status:Hybrid
Publisher DOI:https://doi.org/10.1007/s11587-018-0412-x

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