PDE and mathematical physics · Oct 6, 2026
The planar Mumford–Shah regularity conjecture and local weak-L4 gradient bounds
Resolves the interior regularity conjecture for reduced absolute planar Mumford–Shah minimizers with bounded fidelity data. Locally, the closed discontinuity set is a arc, a regular crack tip, or three arcs meeting at ; only finitely many global connected components meet any compact interior region.
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