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

Article

Abstract.

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:

49J52 

Keywords:

free-discontinuity problems gradient flow slope homogenization non-smooth analysis 

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Copyright information

© Birkhäuser Verlag, Basel 2006

Authors and Affiliations

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

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