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On a method to subtract off a singularity at a corner for the Dirichlet or Neumann problem

Author: Neil M. Wigley
Journal: Math. Comp. 23 (1969), 395-401
MSC: Primary 65.66
MathSciNet review: 0245223
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Abstract: Let $ D$ be a plane domain partly bounded by two line segments which meet at the origin and form there an interior angle $ \pi \alpha > 0$. Let $ U(x,y)$ be a solution in $ D$ of Poisson's equation such that either $ U$ or $ \partial U/\partial n$ (the normal derivative) takes prescribed values on the boundary segments. Let $ U(x,y)$ be sufficiently smooth away from the corner and bounded at the corner. Then for each positive integer $ N$ there exists a function $ {V_N}(x,y)$ which satisfies a related Poisson equation and which satisfies related boundary conditions such that $ U - {V_N}$ is $ N$-times continuously differentiable at the corner. If $ 1/\alpha $ is an integer $ {V_N}$ may be found explicitly in terms of the data of the problem for $ U$.

References [Enhancements On Off] (What's this?)

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Article copyright: © Copyright 1969 American Mathematical Society