Tensorization of Cheeger energies, the space \(H^{1, 1}\) and the area formula for graphs

DOI10.1016/j.aim.2015.06.004zbMath1345.46025arXiv1407.3489OpenAlexW1843069826MaRDI QIDQ2354388

Gareth Speight, Andrea Pinamonti, Luigi Ambrosio

Publication date: 13 July 2015

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

Full work available at URL: https://arxiv.org/abs/1407.3489

zbMATH Keywords

Sobolev spacesarea formulametric measure spacestensorization

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Analysis on metric spaces (30L99)

Related Items (18)

Diffusion, optimal transport and Ricci curvature ⋮ Partial derivatives in the nonsmooth setting ⋮ Rigidity and almost rigidity of Sobolev inequalities on compact spaces with lower Ricci curvature bounds ⋮ Sobolev spaces on warped products ⋮ Regularity of solutions to the fractional Cheeger-Laplacian on domains in metric spaces of bounded geometry ⋮ On master test plans for the space of BV functions ⋮ Harmonic functions with BMO traces and their limiting behaviors on metric measure spaces ⋮ Subgraphs of BV functions on RCD spaces ⋮ About the general chain rule for functions of bounded variation ⋮ Curvewise characterizations of minimal upper gradients and the construction of a Sobolev differential ⋮ Polya-Szego inequality and Dirichlet \(p\)-spectral gap for non-smooth spaces with Ricci curvature bounded below ⋮ Perimeter as relaxed Minkowski content in metric measure spaces ⋮ Weighted Sobolev spaces on metric measure spaces ⋮ Strict and pointwise convergence of BV functions in metric spaces ⋮ From volume cone to metric cone in the nonsmooth setting ⋮ The total variation flow in metric random walk spaces ⋮ Characterisation of upper gradients on the weighted Euclidean space and applications ⋮ Stability and continuity of functions of least gradient

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces
• Regularity of minimizers of the area functional in metric spaces
• Semmes family of curves and a characterization of functions of bounded variation in terms of curves
• Functions of bounded variation on ``good metric spaces
• Differentiability of Lipschitz functions on metric measure spaces
• Axiomatic theory of Sobolev spaces
• Newtonian spaces: An extension of Sobolev spaces to metric measure spaces
• Equivalent definitions of \(BV\) space and of total variation on metric measure spaces
• The continuity equation on metric measure spaces
• 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
• Nonsmooth calculus
• The $p$-weak gradient depends on $p$
• Sobolev met Poincaré
• Sobolev Spaces on Metric Measure Spaces

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