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- W5151176 abstract "This chapter discusses the reduction of the Dirichlet problem and the Neumann problem to integral equations. It highlights that the theorem that the solution of the Dirichlet problem, internal or external, is unique. It follows from the principle of the maximum. The difference of two distinct solutions, if they existed, would in the case of the internal problem be a harmonic function equal to zero on S ; in the case of the external problem, the difference of the two solutions would be harmonic and zero on S and at infinity. Hence, in both cases the difference of the two solutions is always zero. A solution of the external Neumann problem, which has continuous first-order derivatives right up to the boundary, is unique and is determined within an arbitrary additive constant." @default.
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- W5151176 date "1964-01-01" @default.
- W5151176 modified "2023-09-27" @default.
- W5151176 title "REDUCTION OF THE DIRICHLET PROBLEM AND THE NEUMANN PROBLEM TO INTEGRAL EQUATIONS" @default.
- W5151176 doi "https://doi.org/10.1016/b978-0-08-010424-9.50022-6" @default.
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