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

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

2004-10-25

arxiv.org/abs/math/0410525v1

Mathematics

Analysis of PDEs

Scientific paper

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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