Minimal Lipschitz and ∞-harmonic extensions of vector-valued functions on finite graphs

  title={Minimal Lipschitz and ∞-harmonic extensions of vector-valued functions on finite graphs},
  author={Miroslav Bavc'ak and Johannes Hertrich and Sebastian Neumayer and Gabriele Steidl},
  journal={Information and Inference: A Journal of the IMA},
This paper deals with extensions of vector-valued functions on finite graphs fulfilling distinguished minimality properties. We show that so-called $\mathrm{lex}$ and $L\mbox{-}\mathrm{lex}$ minimal extensions are actually the same and call them minimal Lipschitz extensions. Then, we prove that the solution of the graph $p$-Laplacians converge to these extensions as $p\to \infty$. Furthermore, we examine the relation between minimal Lipschitz extensions and iterated weighted midrange filters… 
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