Let D be a domain in R^n for n>=3. Then the transformation v(x_1^, , ..., x_n^, ) = (a/r')^(n - 2) u((a^2 x_1^, )/r^(, 2), ..., (a^2 x_n^, )/r^(, 2)) onto a domain D', where r^(, 2) = x_1^, ^2 + ... + x_n^, ^2 is called a Kelvin transformation. If u(x_1, ..., x_n) is a harmonic function on D, then v(x_1^, , ..., x_n^, ) is also harmonic on D'.
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