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Dirichlet's problem for a body limited by two intersecting spherical surfaces

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Summary

The solution of the internal and external Dirichlet problem is given without assuming rotational symmetry for a body, limited by two intersecting spherical surfaces. The problem is treated in a toroidal system of co-ordinates, using the generalized Mehler integral transform. The results are compared with the solution, presented by Lebedev [1] for the case of rotational symmetry.

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References

  1. Н. Н. Лебедев: Специальные функции и их приложения. Гос. изд. физ.-мат. лит., М.-Л. 1963.

  2. W. Magnus, F. Oberhettinger, R. P. Soni: Formulas and Theorems for the Special Functions of Mathematical Physics. Springer-Vlg., Berlin etc. 1966.

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Authors and Affiliations

  1. Geophysical Institute, Slovak Acad. Sci., Bratislava

    Klement Rosa

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  1. Klement Rosa
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Rosa, K. Dirichlet's problem for a body limited by two intersecting spherical surfaces. Stud Geophys Geod 21, 236–241 (1977). https://doi.org/10.1007/BF01613250

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  • DOI: https://doi.org/10.1007/BF01613250

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