Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 326 / 1 / b / Solution

An element $u^{†}$ is a $J$-minimizing solution whenIt satisfies the source condition in variational regularization when there is a $w^{†}\in Y^{\ast }$ such thatwhere $\partial J(u^{†})$ is the subdifferential of the convex functional $J$.