A short proof of the existence of master test plans

DOI10.1007/S00013-022-01796-0OpenAlexW4310864179MaRDI QIDQ2678889

Enrico Pasqualetto

Publication date: 25 January 2023

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2203.02736

zbMATH Keywords

Sobolev spacemetric measure spacetest planweak upper gradient

Mathematics Subject Classification ID

Nonsmooth analysis (49J52) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Analysis on metric spaces (30L99) Sobolev (and similar kinds of) spaces of functions on metric spaces; analysis on metric spaces (46E36)

Cites Work

• Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces
• Newtonian spaces: An extension of Sobolev spaces to metric measure spaces
• Infinitesimal hilbertianity of locally \(\mathrm{CAT}(\kappa)\)-spaces
• A first-order condition for the independence on \(p\) of weak gradients
• Lectures on nonsmooth differential geometry
• Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below
• Metric measure spaces with Riemannian Ricci curvature bounded from below
• On the differential structure of metric measure spaces and applications
• Sobolev spaces in metric measure spaces: reflexivity and lower semicontinuity of slope
• Nonsmooth calculus
• Testing the Sobolev property with a single test plan
• On master test plans for the space of BV functions

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