\(C^ 2\)-regularity for partially free minimal surfaces
The main result of this paper is the following theorem: ''Let S be an admissable supporting surface of class \(C^{m,\mu}\) (m\(\in N\), \(m\geq 2\), \(0\leq \mu \leq 1)\) and let x be a stationary minimal surface on \(Q^+=\{(u,v)| | u| <1,\quad 0<v<1\}.\) Then \(x\in C^{m,\mu}(Q^+\cup I)\), if \(0<\mu <1\); \(x\in C^{m- 1,\gamma}(Q^+\cup I)\) for every \(\gamma\in (0,1)\), if \(\mu =0\); \(x\in C^{m,\gamma}(Q^+\cup I)\) for every \(\gamma\in (0,1)\), if \(\mu =1\), where \(I=(-1,1)\times \{0\}''\).
scientific article; zbMATH DE number 3899648
scientific article