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On Harmonic Continuation of Differentiable Functions Defined on Part of the Boundary

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Abstract

We establish an explicit formula for reconstruction of a harmonic function in a domain from its values and the values of its normal derivative on part of the boundary; i.e., we give an explicit solution to the Cauchy problem for the Laplace equation.

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Authors and Affiliations

  1. Navoi Samarkand State University, Russia

    Sh. Yarmukhamedov

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  1. Sh. Yarmukhamedov
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Yarmukhamedov, S. On Harmonic Continuation of Differentiable Functions Defined on Part of the Boundary. Siberian Mathematical Journal 43, 183–193 (2001). https://doi.org/10.1023/A:1013849310522

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