Geodesic
Existence of Solutions to Poisson's Equation
Canadian mathematical bulletin, Tome 51 (2008) no. 2, pp. 229-235

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DOI

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.
DOI : 10.4153/CMB-2008-024-8
Mots-clés : 31B25 
Hanley, Mary. Existence of Solutions to Poisson's Equation. Canadian mathematical bulletin, Tome 51 (2008) no. 2, pp. 229-235. doi: 10.4153/CMB-2008-024-8
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     author = {Hanley, Mary},
     title = {Existence of {Solutions} to {Poisson's} {Equation}},
     journal = {Canadian mathematical bulletin},
     pages = {229--235},
     year = {2008},
     volume = {51},
     number = {2},
     doi = {10.4153/CMB-2008-024-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2008-024-8/}
}
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