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arXiv · 2109.08436

$p$-harmonic mappings between metric spaces

Chang-Yu Guo·Manzi Huang·Zhuang Wang·Haiqing Xu
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Abstract

In this paper, we solve the Dirichlet problem for Sobolev maps between singular metric spaces that extends the corresponding result of Guo and Wenger [Comm. Anal. Geom. 2020]. The main new ingredient in our proofs is a suitable extension of the theory of trace for metric valued Sobolev maps developed by Korevaar and Schoen [Comm. Anal. Geom. 1993]. We also develop a theory of trace in the borderline case, which investigates a sharp condition to characterize the existence of traces.

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Chang-Yu Guo, Manzi Huang, Zhuang Wang, Haiqing Xu. 2021-09-17. $p$-harmonic mappings between metric spaces. https://arxiv.org/abs/2109.08436

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