2. Consider the minimisation problem find u € V such that J(u) s J(v) Vue V, where J: H(0,1) Ris the functional defined by (3) J(n) := Gºrd- S fndx, with f € L*(0,1) and V := {v € H(0, 1) ["(0) = v(1) = 0 and v' (O) = v'(1) = 0). (ii) Hence prove that the minimisation problem (3) has a unique solution. You may use without proof the fact that linally := ||"||220.1) defines a norm on V. (111) wu ..he