Laplace's Equation

Laplace's Equation:

Consider Laplace equations in two variables on the upper half - plane y > 0. Then

Let the boundary conditions;

be given for a function f ∈ L¹ (R). Then taking the Fourier transform in the variables x,

We need to condition to determine the functions A (ξ), B (ξ). In addition to u (x, 0) = f (x), -

Hence,