article

Title: $p$-Harmonic approximation of functions of least gradient

Authors: Petri Juutinen

Issue: Volume 54 (2005), Issue 4, 1015-1030

Abstract:

$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 $BV(\Omega)$.$