1. (a) Show that 27 1 1 n-2 log|2| if n = 2, n(x) = if n e N, n > 3. n(n-2)vol(B1(0)) solves the Laplace equation in R\{0}. (b) Given f C2(R3) with compact support show that u(t) = n(y x)f(y)dy solves the Poisson equation Au f on R3. Hint: Follow the proof of the Representation formula. 1. (a) Show that 27 1 1 n-2 log|2| if n = 2, n(x) = if n e N, n > 3. n(n-2)vol(B1(0)) solves the Laplace equation in R\{0}. (b) Given f C2(R3) with compact support show that u(t) = n(y x)f(y)dy solves the Poisson equation Au f on R3. Hint: Follow the proof of the Representation formula