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