Γ-convergence

Summary

Γ-convergence is a notion of convergence for functionals that is designed for minimization problems. A sequence $F_n$ Γ-converges to $F$ when two things hold. A lower bound inequality holds along every convergent sequence of points, and the bound is reached along some sequence. Under a compactness condition, minimum values and minimizers of $F_n$ then converge to those of $F$. It was introduced by Ennio De Giorgi. It is the standard tool to pass from a family of variational problems to a limit problem, as in homogenization and phase transitions. The definition gives the precise conditions.