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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Mean boundary value problems for a class of elliptic equations in $ E\sp{3}$


Author: Peter A. McCoy
Journal: Proc. Amer. Math. Soc. 76 (1979), 123-128
MSC: Primary 35C10; Secondary 35J99
MathSciNet review: 534401
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Abstract: An interior Dirichlet problem for generalized axisymmetric potentials is solved constructively by means of a Riemann series expansion determined from the arithmetic means of the boundary values. The problem is generalized to a class of axisymmetric elliptic partial differential equations in $ {E^3}$. The Bergman and Gilbert integral operator method is used along with the method of ascent.


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DOI: https://doi.org/10.1090/S0002-9939-1979-0534401-7
Keywords: Generalized axisymmetric potentials, Bergman and Gilbert integral operator method, Dirichlet problem, elliptic equations in $ {E^3}$, method of ascent
Article copyright: © Copyright 1979 American Mathematical Society