9. (a) We call Laplacian the operator 22 + dy? 22 A Let u(x, y, z) be a twice differentiable function. Show that Au = div(Vu). (b) Let BC R³ be the closed unit ball a2 +y? +2² < 1 and S2 the unit sphere x²+ y? +z² = 1. Suppose that the function u(x, Y, 2) satisfies Au = 0 in B and Vu · n n S² . (1) on (i) Compute Vu ·n dS . S2

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