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  • https://math.libretexts.org/Bookshelves/Differential_Equations/Introduction_to_Partial_Differential_Equations_(Herman)/08%3A_Complex_Representations_of_Functions/8.06%3A_Laplaces_Equation_in_2D_Revisited
    Harmonic functions are solutions of Laplace’s equation. We have seen that the real and imaginary parts of a holomorphic function are harmonic. So, there must be a connection between complex functions ...Harmonic functions are solutions of Laplace’s equation. We have seen that the real and imaginary parts of a holomorphic function are harmonic. So, there must be a connection between complex functions and solutions of the two-dimensional Laplace equation. In this section we will describe how conformal mapping can be used to find solutions of Laplace’s equation in two dimensional regions.

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