9. (a) We call Laplacian the operator A dx2 dy? Let u(x, y, z) be a twice differentiable function. Show that Δυ - div(Vu). (b) Let BCR³ be the closed unit ball x? +y? + 22

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Extracted text: 9. (a) We call Laplacian the operator A dx2 dy? Let u(x, y, z) be a twice differentiable function. Show that Δυ - div(Vu). (b) Let BCR³ be the closed unit ball x? +y? + 22 <1 and="" s²="" the="" unit="" sphere="" x?="" +y?="" +="" 22="1." suppose="" that="" the="" function="" u(x,="" y,="" z)="" satisfies="" δυ="" 0="" in="" b="" and="" vu="" ·="" n="" 1="" on="" s2.="" (1)="" (i)="" compute="" vu="" ·="" n="" ds="" .="" s2="" (ii)="" can="" there="" exist="" a="" function="" u="" satisfying="" the="" problem="">