A sharp pointwise bound for functions with $L\sp 2$-Laplacians on arbitrary domains and its applications
| Autor: | Xie, Wenzheng |
|---|---|
| Zdroj: | Bulletin of the American Mathematical Society; April 1992, Vol. 26 Issue: 2 p294-298, 5p |
| Abstrakt: | For all functions on an arbitrary open set $ \Omega \subset {R^3}$ $\displaystyle \mathop {{\text{sup}}}\limits_\Omega \vert u\vert \leq {(2\pi )^{... ... }\vert\nabla u{\vert^2}dx{\smallint _\Omega }\vert\Delta u{\vert^2}dx)^{1/4}}.$ The method of proof is elementary and admits generalizations. The inequality is applied to establish an existence theorem for the Burgers equation. |
| Databáze: | Supplemental Index |
| Externí odkaz: |
|