Preprint
Inserted: 24 oct 2026
Last Updated: 24 oct 2026
Year: 2026
Abstract:
We give a short proof that the planar cracktip is a global minimizer of the Mumford--Shah functional, based on interior and Dirichlet boundary regularity. We construct a Dirichlet minimizer with nonempty discontinuity set and show that this set contains no simple closed curves. The regularity results then imply the existence of an interior regular loose end, at which a blow-up yields the cracktip.
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