Infinity-Laplacians on Scalar- and Vector-Valued Functions and Optimal Lipschitz Extensions on Graphs

10/25/2019 ∙ by Johannes Hertrich, et al. ∙ 0

Extending functions from boundary values plays an important role in various applications. In this thesis we consider discrete and continuous formulations of the problem based on p-Laplacians, in particular for p=∞ and tight Lipschitz extensions. The thesis gives an overview of the existing theory and provides some novel results on the approximation of tight Lipschitz extensions for vector-valued functions.

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