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arxiv: math/0410525 · v1 · submitted 2004-10-25 · 🧮 math.AP

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

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keywords functionalslopemumford-shahnotionunilateralcasecorrespondingcracks
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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.

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