A <weak local minimizer of a variational integral> is an admissible $\bar u$ for which some $\rho>0$ makes $I(v)\geq I(\bar u)$ whenever $v\in\mathcal A$ and $\|v-\bar u\|_{W^{1,\infty}}<\rho$. Both the <function> and its <derivative> are required to be close.

Solution

Past exam of the calculus of variations course of the University of Oxford / 2009 / 3 / a / i / Solution

 Solution (source code)