Variational approximation of a functional of Mumford–Shah type in codimension higher than one. (6th February 2014) - Ghiraldin, Francesco
Abstract : In this paper we consider a new kind of Mumford–Shah functional E ( u, Ω ) for maps u : ℝ m  → ℝ n with m  ≥  n . The most important novelty is that the energy features a singular set S u 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].