A sharp pointwise bound for functions with $L^2$-Laplacians on arbitrary domains and its applications
| dc.creator | Xie, Wenzheng | |
| dc.date | 1992-04-01 | |
| dc.date.accessioned | 2026-07-07T09:14:46Z | |
| dc.date.available | 2026-07-07T09:14:46Z | |
| dc.description | For all functions on an arbitrary open set $Ω\subset\R^3$ with zero boundary values, we prove the optimal bound \[ \sup_Ω|u| \leq (2π)^{-1/2} \left(\int_Ω|\nabla u|^2 \,dx\, \int_Ω|Δu|^2 \,dx\right)^{1/4}. \] The method of proof is elementary and admits generalizations. The inequality is applied to establish an existence theorem for the Burgers equation. | |
| dc.description | 5 pages | |
| dc.identifier | https://arxiv.org/abs/math/9204239 | |
| dc.identifier | http://arxiv.org/abs/math/9204239 | |
| dc.identifier | Bull. Amer. Math. Soc. (N.S.) 26 (1992) 294-298 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152797 | |
| dc.subject | Analysis of PDEs | |
| dc.title | A sharp pointwise bound for functions with $L^2$-Laplacians on arbitrary domains and its applications | |
| dc.type | text |