Variational approximation of a functional of Mumford–Shah type in codimension higher than one

In this paper we consider a new kind of Mumford–Shah functional E(u, Ω) for maps u : ℝm → ℝn with m ≥ n. The most important novelty is that the energy features a singular set Su of codimension greater than one, defined through the theory of distributional jacobians. After recalling the basic definitions and some well established results, we prove an approximation property for the energy E(u, Ω) via Γ −convergence, in the same spirit of the work by Ambrosio and Tortorelli [L. Ambrosio and V.M. Tortorelli, Commun. Pure Appl. Math. 43 (1990) 999–1036]