Integral representations and $L^\infty$ bounds for solutions of the Helmholtz equation on arbitrary open sets in $\mathbb{R}^2$ and $\mathbb{R}^3$
| Autor: | Xie, Wenzheng |
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| Rok vydání: | 1995 |
| Předmět: | |
| Zdroj: | Differential Integral Equations 8, no. 3 (1995), 689-698 |
| ISSN: | 0893-4983 |
| DOI: | 10.57262/die/1369316516 |
| Popis: | We establish sharp $L^{\infty}$ bounds for functions defined on arbitrary open sets in $\Bbb R^2$ and $\Bbb R^3$, which vanish on the boundary and have $L^2$ Laplacians. All functions corresponding to the best possible constants are explicitly given. The proof is based on integral representations using the Green's function for the Helmholtz equation in arbitrary domains. |
| Databáze: | OpenAIRE |
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