p-Harmonic mappings between metric spaces

In this paper, we solve the Dirichlet problem for Sobolev maps between singular metric spaces that extends corresponding result of Guo and Wenger (Commun Anal Geom 28(1):89–112, 2020). The main new ingredient in our proofs is a suitable extension theory trace valued developed by Korevaar Schoen 1(3–4):561–659, 1993) . We also develop borderline case, which investigates sharp condition to characterize existence traces.