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Search: MSC category 31B25 ( Boundary behavior )

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1. CMB 2009 (vol 52 pp. 555)

Hirata, Kentaro
 Boundary Behavior of Solutions of the Helmholtz Equation This paper is concerned with the boundary behavior of solutions of the Helmholtz equation in $\mathbb{R}^\di$. In particular, we give a Littlewood-type theorem to show that the approach region introduced by Kor\'anyi and Taylor (1983) is best possible. Keywords:boundary behavior, Helmholtz equationCategories:31B25, 35J05

2. CMB 2008 (vol 51 pp. 229)

Hanley, Mary
 Existence of Solutions to Poisson's Equation 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. Category:31B25
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