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Jacobi fields and regularity of functions of least gradients. (English) Zbl 0605.49027
The authors prove regularity for functions of least gradient. Let \(\Omega \subset {\mathbb{R}}^ n\) be bounded and open, \(2\leq n\leq 7\), and let \(\partial \Omega\) be a class n-1 submanifold of \({\mathbb{R}}^ n\), \(\phi\) :\(\partial \Omega \to {\mathbb{R}}\) of class n-1. If \(u: {\bar \Omega}\to {\mathbb{R}}^ n\) is Lipschitzian and of least gradient with \(u=\phi\) on \(\partial \Omega\), then there exists an open dense set \(W\subset \Omega\) such that u/W is of class (n-3).
Reviewer: G.Dziuk

MSC:
49Q05 Minimal surfaces and optimization
26B30 Absolutely continuous real functions of several variables, functions of bounded variation
49Q20 Variational problems in a geometric measure-theoretic setting
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
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