Nonlinear Differential Equations and Applications NoDEA

, Volume 13, Issue 5, pp 713–734

On a notion of unilateral slope for the Mumford-Shah functional


DOI: 10.1007/s00030-006-4054-4

Cite this article as:
Maso, G.D. & Toader, R. Nonlinear differ. equ. appl. (2007) 13: 713. doi:10.1007/s00030-006-4054-4


In this paper we introduce a notion of unilateral slope for the Mumford-Shah functional, and provide an explicit formula in the case of smooth cracks. We show that the slope is not lower semicontinuous and study the corresponding relaxed functional.

2000 Mathematics Subject Classification:



free-discontinuity problemsgradient flowslopehomogenizationnon-smooth analysis

Copyright information

© Birkhäuser Verlag, Basel 2006

Authors and Affiliations

  1. 1.SISSATriesteItaly
  2. 2.Dipartimento di Ingegneria CivileUniversità di UdineUdineItaly