A growth estimate for the planar Mumford--Shah minimizers at a tip point: An alternative proof of David--L\'eger
Year: 2025
Type: preprint
Abstract: Let $\Omega\subset \mathbb R^2$ be a bounded domain and $u\in SBV(\Omega)$ be a local minimizer of the Mumford--Shah problem in the plane, with $0\in \overline{S}_u$ being a tip point and $B_1\subset \Omega$. Then there exist absolute constants $C>0$ and $0<r_0<1$ such that $$|u(x)-u(0)|\le C r^{\frac 1 2} \quad \text{ for any } \ x\in B_r \ \text{ and } \ 0<r
Source: arXiv (Cornell University)
Author: Zhang, Yi Ru-Ya
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979307695
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