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On the L∞-maximization of the solution of Poisson's equation: Brezis–Gallouet–Wainger type inequalities and applications
Published online by Cambridge University Press: 20 February 2020
Abstract
For the solution of the Poisson problem with an L∞ right hand side
\begin{cases} -\Delta u(x) = f (x) & {\rm in}\ D, \\ u=0 & {\rm on}\ \partial D \end{cases}
\|u\|_\infty\leq \|f\|_\infty \sigma_D(\|f\|_1/\|f\|_\infty),
$\|f\|_1$ and
$\|f\|_\infty .$ We also show that
\sigma_D(t)\leq\sigma_B(t),\text{ for }t\in[0,|D|],
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MSC classification
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- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 151 , Issue 1 , February 2021 , pp. 79 - 92
- Copyright
- Copyright © The Author(s) 2020. Published by The Royal Society of Edinburgh
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