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- W2064304157 abstract "Introduction. The method which involves the application of the properties of the Cauchy and Schwarz integrals in order to obtain the solutions to the two-dimensional problems of potential theory and elasticity in regions either internal or external to a closed plane curve has been developed by Muskhelishvili [1, 2]. It is the object of the present paper to apply this method to determine solutions to the two-dimensional boundary value problems of the internal-external type associated with a circle, when the controlling differential equation is of the Poisson type. By way of illustration a boundary value problem of the third type is considered. The center of a circle C of radius a is assumed to be located at the origin 0 of polar coordinates (r, 0), covering the regions Se Si , respectively external and internal to C. It is required to determine functions 0e(r, 0), 4i(r, 0), defined in the regions Se , Si respectively, which possess given singularities in these regions and satisfy the Poisson partial differential equations" @default.
- W2064304157 created "2016-06-24" @default.
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- W2064304157 date "1962-12-01" @default.
- W2064304157 modified "2023-09-25" @default.
- W2064304157 title "Some Solutions of an Internal-External Problem of the Third Type for a Circle" @default.
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- W2064304157 doi "https://doi.org/10.1137/0110049" @default.
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