Korevaar–Schoen's energy on strongly rectifiable spaces

We extend Korevaar-Schoen’s theory of metric valued Sobolev maps to cover the case of the source space being an RCD-space. When the target space is CAT(0) we establish that the corresponding energy functional is convex, lower semicontinuous and admits a unique minimizer, in line with the smooth situation. The talk is based on the joined work: Nicola Gigli, Alexander Tyulenev, “Korevaar–Schoen's energy on strongly rectifiable spaces”, Calc. Var. Partial Differential Equations, 60 (2021), 235, 54 pp., arXiv: 2002.07440