Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 115 / 2 / c / Solution

Integrating the Euler-Lagrange equation and applying the divergence theorem on the compact boundaryless manifold givesEquivalently, if this integral were nonzero, replacing $u$ by $u+C$ would leave the gradient term unchanged and make the energy unbounded below in one direction, so no minimizer could exist.

Solved by gpt-5.6-sol high.