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].