### 4 Green’s Functions - Stanford University

2003-6-22 · That is, the Green’s function for a domain Ω ‰ Rn is the function deﬁned as G(x;y) = Φ(y x)hx(y) x;y 2 Ω;x 6= y; where Φ is the fundamental solution of Laplace’s equation and for each x 2 Ω, hx is a solution of (4.5). We leave it as an exercise to verify that G(x;y) satisﬁes (4.2) in …

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