# Difference between the fundamental solution and the Green function

A lot of sources (books, internet courses, articles etc.) deal with just one of the two: Green function, and the fundamental solution. I wasn't able to find a distinction, but I suppose there is one. However both seem to be defined for a differential operator $D$ as follows:

$G(x-y)$ such, that: $DG(x-y)=\delta(y)$

So what's the difference?

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Fundamental solution solves $DG(x-y)=\delta(y)$ on the entire space $\mathbb R^n$.
Green's function solves $DG(x-y)=\delta(y)$ on some domain $\Omega\subset \mathbb R^n$, and satisfies some homogeneous boundary condition. (Most often, but not always, the Dirichlet condition).