Calculus of Variations and Geometric Measure Theory

N. Gigli - F. Nobili

A first-order condition for the independence on $p$ of weak gradients

created by nobili on 28 Dec 2021
modified on 28 Aug 2022

[BibTeX]

Published Paper

Inserted: 28 dec 2021
Last Updated: 28 aug 2022

Journal: J. Funct. Anal.
Year: 2022
Doi: https://doi.org/10.1016/j.jfa.2022.109686

ArXiv: 2112.12849 PDF

Abstract:

It is well known that on arbitrary metric measure spaces, the notion of minimal $p$-weak upper gradient may depend on $p$. In this paper we investigate how a first-order condition of the metric-measure structure, that we call Bounded Interpolation Property, guarantees that in fact such dependence is not present. We also show that the Bounded Interpolation Property is stable for pointed measure Gromov Hausdorff convergence and holds on a large class of spaces satisfying curvature dimension conditions.