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1. CMB 2009 (vol 52 pp. 555)
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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 equation Categories:31B25, 35J05 |
2. CMB 2008 (vol 51 pp. 229)
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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 |