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4 Green’s Functions - Stanford University
web.stanford.eduThat 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 the sense of distributions. Conclusion: If ...
GREEN’S FUNCTION FOR LAPLACIAN - University of Michigan
math.lsa.umich.eduGREEN’S FUNCTION FOR LAPLACIAN 3 finally we arrive at 1 = 2πRΓ′(R) this gives that Γ′(R) = 1 2πR, therefore Γ(R) = 1 2π lnR. In other wards, an application of divergence theorem also gives us the same answer as above, with the constant c1 = 1 2π.