Question 2 [20 marks] Consider V2u = f(x), xen CR" (bounded), Blu + $2 Vu . n = g(x), x E an, (1) with 31, 32 ER. a) Let & E R" arbitrary but fixed. Let G(x; {) be the solution to (1) with f (x) = 6(x; {) and g(x) = 0, where o(x; {) is the Dirac delta function. Show that G is symmetric in its arguments, i.e., G(x; {) = G({; x). Assume B1 * 0, 82 / 0 [6 marks]. b) Show that for G(x, {), we have VaG(u, v) = VG(v, u), where u, v E S [4 marks]. (Hint: use the limit definition of partial derivatives)