(a) Consider a function f (x, y) of class C4. Show that if we apply the Laplacian operator ∇2 = ∂2/∂x2 + ∂2/∂y2 twice to f, we obtain
(b) Now suppose that f is a function of n variables of class C4. Show that
Functions that satisfy the partial differential equation ∇2 (∇2 f ) = 0 are called biharmonic functions and arise in the theoretical study of elasticity.
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