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On the minima of functionals with linear growth. (English) Zbl 0589.49027
Let u be a minimum point for a functional with linear growth. The author studies the trace on the singular support of Du of some vectorfields associated to u such as, for example, \(N=Du/\sqrt{1+| Du|^ 2}\). He proves that the averages \(N_{\rho}\) of N on the ball \(B_{\rho}(x)\) converge to Du/\(| Du|\) in integral mean with respect to the measure \(| Du|\) on the set where Du is singular.
Reviewer: R.Schianchi

MSC:
49Q20 Variational problems in a geometric measure-theoretic setting
28A75 Length, area, volume, other geometric measure theory
58C25 Differentiable maps on manifolds
58K99 Theory of singularities and catastrophe theory
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