The Gradient of a Solution of the Poisson Equation in the Unit Ball and Related Operators
In this paper we determine the ${{L}^{1}}\to {{L}^{1}}$ and ${{L}^{\infty }}\to {{L}^{\infty }}$ norms of an integral operator $\mathcal{N}$ related to the gradient of the solution of Poisson equation in the unit ball with vanishing boundary data in sense of distributions.
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| Veröffentlicht in: | Canadian mathematical bulletin 2017-09, Vol.60 (3), p.536-545 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | In this paper we determine the
${{L}^{1}}\to {{L}^{1}}$
and
${{L}^{\infty }}\to {{L}^{\infty }}$
norms of an integral operator
$\mathcal{N}$
related to the gradient of the solution of Poisson equation in the unit ball with vanishing boundary data in sense of distributions. |
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| ISSN: | 0008-4395 1496-4287 |
| DOI: | 10.4153/CMB-2017-020-7 |