I'm trying to understand the derivation for methods of Greens functions for PDEs but I can't get my head around some parts. I'm starting to feel comfortable with the method itself but I want to understand why it works.(adsbygoogle = window.adsbygoogle || []).push({});

The thing I have problem with is quite crucial and it is the following:

I have the general problem ##-\Delta u=0## in the upper half plane and some boundary condition ##g(x)## on the ##x##-axis itself. Why is it enough to solve ##-\Delta u=0## for ##y>0## and ##u(x,o)=\delta(x)## and then use the convolution to get the solution for the original problem? I have the whole derivation in front of me but I can't get a intuitive feeling about what is going on with the delta function, how can one just replace the boundary condition with a Dirac's delta and still get a solution that works for an arbitrary ##g(x)##?

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# Understanding the method of Green's function

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