$p$-harmonic mappings between metric spaces
Analysis of PDEs
2022-08-17 v1 Metric Geometry
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.
Keywords
Cite
@article{arxiv.2109.08436,
title = {$p$-harmonic mappings between metric spaces},
author = {Chang-Yu Guo and Manzi Huang and Zhuang Wang and Haiqing Xu},
journal= {arXiv preprint arXiv:2109.08436},
year = {2022}
}