Korevaar-Schoen-Sobolev spaces and critical exponents in metric measure spaces

Abstract

We present developments in the theory of Korevaar-Schoen-Sobolev spaces on metric measure spaces. While this theory coincides with those of Cheeger and Shanmugalingam if the space is doubling and satisfies a Poincaré inequality, it offers new perspectives in the context of fractals for which the approach by weak upper gradients is inadequate.

arXiv commentPrevious version of the manuscript was used as Lecture Notes for the mini course hold at Texas A&M during the workshop Geometry and Analysis on Nonsmooth Spaces, August 8-12 2022. v6: Final version to appear in Ann. Fenn