Duality properties of metric Sobolev spaces and capacity

DOI10.3934/mine.2021001zbMath1504.46048OpenAlexW3045407123MaRDI QIDQ2167432

Giuseppe Savaré, Luigi Ambrosio

Publication date: 25 August 2022

Published in: Mathematics in Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/mine.2021001

zbMATH Keywords

capacitycapacitary measuresdual Cheeger energydynamic transport plansmetric Sobolev spacesmodulus of a family of rectifiable curves

Mathematics Subject Classification ID

Potentials and capacities on other spaces (31C15) Sobolev (and similar kinds of) spaces of functions on metric spaces; analysis on metric spaces (46E36)

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Cites Work

• Optimal transport, Cheeger energies and contractivity of dynamic transport distances in extended spaces
• Weak and strong convergence of derivations and stability of flows with respect to MGH convergence
• Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces
• On the duality between \(p\)-modulus and probability measures
• Nonlinear potential theory on metric spaces
• Extremal length and functional completion
• Functional analysis, Sobolev spaces and partial differential equations
• Differentiability of Lipschitz functions on metric measure spaces
• Newtonian spaces: An extension of Sobolev spaces to metric measure spaces
• Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below
• Characterization of the subdifferentials of convex functions
• Sobolev Spaces on Metric Measure Spaces
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