Gamma-convergence ($F_n\stackrel{\Gamma }{\to }F$)

A sequence of functionals Gamma-converges in a specified topology when every convergent $u_n\to u$ satisfies $F(u)\le {\mathrm{liminf}}_n{F}_n(u_n)$, and each $u$ has a recovery sequence $u_n\to u$ with $F_n(u_n)\to F(u)$. With appropriate compactness of energy sublevels, limits of approximate global minimizers minimize $F$, and the minimum values converge. This is suited to variational approximation such as the Ambrosio–Tortorelli approximation; it does not describe arbitrary local minima.