Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W7223447256