$p$-Harmonic approximation of functions of least gradient Petri Juutinen 49Q2035B40function of least gradientp-Laplacian The purpose of this note is to establish a natural connection between the minimizers of two closely related variational problems. We prove global and local convergence results for the $p$-harmonic functions, defined as continuous local minimizers of the $L^{p}$ norm of the gradient for $1<p<\infty$, as $p\to 1$, and show that the limit function minimizes at least locally the total variation of the vector-valued measure $ abla u$ in $BV(\Omega)$. Indiana University Mathematics Journal 2005 text pdf 10.1512/iumj.2005.54.2658 10.1512/iumj.2005.54.2658 en Indiana Univ. Math. J. 54 (2005) 1015 - 1030 state-of-the-art mathematics http://iumj.org/access/