Sobolev Spaces on Metric Measure Spaces: An Approach Based on Upper Gradients

492 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Uniformization of two-dimensional metric surfaces (2014, background): “∈ L2(Y) is a weak upper gradient of F, then there exists an exceptional set Γ′′ of modulus zero such that if h> 0 is a Borel function in Z, then (67) Z F◦γ hds6 Z γ (h◦F)gds for every γ/∈ Γ′′. See [34] for the proof of this property and more information on upper gradients and absolute continuity.”
Intrinsic structure of minimal discs in metric spaces (2016, methodology): “We assume some experience with Sobolev maps with values in complete metric spaces X and refer the reader to [13; 24].”
Muckenhoupt Ap-properties of Distance Functions and Applications to Hardy–Sobolev -type Inequalities (2017, background): “[3, 16] for introduction on analysis on metric spaces based on the notion of upper gradients.”