On the duality between \(p\)-modulus and probability measures

DOI10.4171/JEMS/546zbMath1331.28005arXiv1311.1381MaRDI QIDQ493140

Giuseppe Savaré, Luigi Ambrosio, Simone Di Marino

Publication date: 11 September 2015

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.1381

zbMATH Keywords

capacitydualitySobolev functions\(p\)-modulus

Mathematics Subject Classification ID

Contents, measures, outer measures, capacities (28A12) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Duality theory (optimization) (49N15)

Related Items (23)

Plans on measures and \textit{AM}-modulus ⋮ Diffusion, optimal transport and Ricci curvature ⋮ Equivalence of two BV classes of functions in metric spaces, and existence of a Semmes family of curves under a 1-Poincaré inequality ⋮ Functions of bounded variation and the \(AM\)-modulus in \(\mathbb{R}^n\) ⋮ The $p$-weak gradient depends on $p$ ⋮ Measure families with the same Fuglede \(p\)-modulus ⋮ Testing the Sobolev property with a single test plan ⋮ Three superposition principles: currents, continuity equations and curves of measures ⋮ Duality properties of metric Sobolev spaces and capacity ⋮ Sobolev Spaces in Extended Metric-Measure Spaces ⋮ AM‐modulus and Hausdorff measure of codimension one in metric measure spaces ⋮ Heat kernels, stochastic processes and functional inequalities. Abstracts from the workshop held October 30 -- November 5, 2022 ⋮ A version of Stokes's theorem using test curves ⋮ Computing the \(p\)-modulus of systems of measures via optimal plans ⋮ Some properties of the extremal function for the Fuglede \(p\)-modulus ⋮ Exact integrability conditions for cotangent vector fields ⋮ Curvewise characterizations of minimal upper gradients and the construction of a Sobolev differential ⋮ An alternative capacity in metric measure spaces ⋮ The Poincaré inequality does not improve with blow-up ⋮ The space of functions of bounded variation on curves in metric measure spaces ⋮ Semmes family of curves and a characterization of functions of bounded variation in terms of curves ⋮ Some remarks on the Fuglede \(p\)-modulus ⋮ Moduli inequalities for W¹_n-1,loc-mappings with weighted bounded (q, p)-distortion

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