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A Note on the Removal of Further Breakdowns in Classical Solutions of Laplace"s Equation on Sectorial Regions

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Abstract

This note considers solutions to Laplace"s equation on sectors with varying vertex angles. Under Neumann conditions on the radial boundaries, there are two critical vertex angles for which classical separable solutions break down. These breakdowns have been noted in the literature and resolved. Here Dirichlet and mixed conditions are also treated. For all three boundary conditions in combination, nine further critical angles are identified and valid corresponding solutions found.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA, 15213-3890, U.S.A

    G.B. Sinclair

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  1. G.B. Sinclair
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Sinclair, G. A Note on the Removal of Further Breakdowns in Classical Solutions of Laplace"s Equation on Sectorial Regions. Journal of Elasticity 56, 247–252 (1999). https://doi.org/10.1023/A:1007659631382

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  • DOI: https://doi.org/10.1023/A:1007659631382

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