The idea of a variational convergence is introduced as an equality of upper and lower bounds for families of variational problems. Examples are given that illustrate some of the main applications of Gamma-convergence, starting from the gradient theory of phase transitions, through homogenization and dimension reduction, to limits of atomistic theories. A final section shows how the definition of Gamma-convergence can be deduced from the requirement that it implies the convergence of minimizers be local and stable under continuous perturbations.
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