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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