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Existence of Solutions to Poisson's Equation

Open Access article
 Printed: Jun 2008
  • Mary Hanley
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Let $\Omega$ be a domain in $\mathbb R^n$ ($n\geq 2$). We find a necessary and sufficient topological condition on $\Omega$ such that, for any measure $\mu$ 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.
MSC Classifications: 31B25 show english descriptions Boundary behavior 31B25 - Boundary behavior

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