On the Lp norm of the torsion function

M. van den Berg*, T. Kappeler

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

153 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 languageEnglish
Pages (from-to)399-414
Number of pages16
JournalRicerche di Matematica
Volume68
Early online date29 Jun 2018
DOIs
Publication statusE-pub ahead of print - 29 Jun 2018

Keywords

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

Fingerprint Dive into the research topics of 'On the <i>L<sup>p</sup></i> norm of the torsion function'. Together they form a unique fingerprint.

Cite this