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Existence of Solutions to Poisson's Equation
Published online by Cambridge University Press: 20 November 2018
Abstract
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Let 
$\Omega$ be a domain in
${{\mathbb{R}}^{n}}\,(n\,\ge \,2).$ We find a necessary and sufficient topological condition on $\Omega$ such that, for any measure 
$ $ on
${{\mathbb{R}}^{n}}$
, there is a function 
$u$ with specified boundary conditions that satisfies the Poisson equation 
$\Delta u\,=\,\mu$ on $\Omega$ in the sense of distributions.
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- Copyright © Canadian Mathematical Society 2008
References
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