Γ-convergence is a concept in the field of mathematical analysis, particularly in the study of functional analysis, calculus of variations, and optimization. It provides a way to analyze the convergence of functionals (typically a sequence of functions or energy functionals) in a manner that is particularly useful when studying minimization problems and variational methods.
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A sequence of functionals Gamma-converges in a specified topology when every convergent satisfies , and each has a recovery sequence with . With appropriate compactness of energy sublevels, limits of approximate global minimizers minimize , and the minimum values converge. This is suited to variational approximation such as the Ambrosio–Tortorelli approximation; it does not describe arbitrary local minima.