On the minima of functionals with linear growth
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.
scientific article; zbMATH DE number 3947022
scientific article