van den Berg, M; Kappeler, Thomas (2019). On the ${ L}^{ p}$ norm of the torsion function. Ricerche di Matematica, 68(2):399-414.
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.
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.
| 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 |
| Scopus Subject Areas: | Physical Sciences > General Mathematics
Physical Sciences > Applied Mathematics |
| Uncontrolled Keywords: | Applied Mathematics, General Mathematics |
| Language: | English |
| Date: | 1 December 2019 |
| Deposited On: | 23 Jan 2019 12:48 |
| Last Modified: | 20 Sep 2023 01:46 |
| Publisher: | Springer |
| ISSN: | 0035-5038 |
| OA Status: | Hybrid |
| Publisher DOI: | https://doi.org/10.1007/s11587-018-0412-x |
van den Berg, M