(a) Show that log |a| if n = 2, Pn(x) if n E N, n >...

 

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