(a) Consider a function f (x, y) of class C4. Show that if we apply the Laplacian operat...

(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.