Calculus of Variations and Geometric Measure Theory

F. Ghiraldin

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

created by ghiraldin on 24 Jan 2013
modified by paolini on 14 Jun 2013


Submitted Paper

Inserted: 24 jan 2013
Last Updated: 14 jun 2013

Journal: ESIAM: COCV
Year: 2013


In this paper we consider a new kind of Mumford-Shah functional $E(u,\Omega)$ for maps $u:\mathbb{R}^m\rightarrow \mathbb{R}^n$ with $m\geq n$. 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 $E(u,\Omega)$ via $\Gamma-$convergence, in the same spirit of the work by Ambrosio and Tortorelli.

Tags: GeMeThNES
Keywords: $\Gamma$-convergence, Jacobian, Ginzburg-Landau, Mumford-Shah