$p$-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
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10.1512/iumj.2005.54.2658
10.1512/iumj.2005.54.2658
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Indiana Univ. Math. J. 54 (2005) 1015 - 1030
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