2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72994In this paper we introduce a notion of unilateral slope for the Mumford-Shah functional, and provide an explicit formula in the case of smooth cracks. We show that the slope is not lower semicontinuous and study the corresponding relaxed functional.Analysis of PDEs49J52On a notion of unilateral slope for the Mumford-Shah functionaltext