2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66687We define a notion of quasi-static evolution for the elliptic approximation of the Mumford-Shah functional proposed by Ambrosio and Tortorelli. Then we prove that this regular evolution converges to a quasi-static growth of brittle fractures in linearly elastic bodies.34 pagesAnalysis of PDEs35R35; 74R10, 35J25text