Variational approximation of a functional of Mumford–Shah type in codimension higher than one. (6th February 2014)

• Record Type: Journal Article
• Authors: Ghiraldin, Francesco
• Is Part Of: ESAIM. Volume 20:Number 1(2014:Jan.)
• Page Start: 190
• Page End: 221
• Publication Date: 2014-02-06
• Subjects: Jacobian, -- Γ-convergence, -- higher codimension, -- Mumford–Shah, -- Ginzburg–Landau, -- phase transition; System analysis -- Periodicals; Calculus of variations -- Periodicals; Mathematical analysis -- Periodicals; Mathematical optimization -- Periodicals; Control theory -- Periodicals; 515.64
• DOI: 10.1051/cocv/2013061
• Languages: English
• ISSNs: 1292-8119

Abstract

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].