Metric Sobolev spaces. I: Equivalence of definitions (Q6655896)

scientific article; zbMATH DE number 7960925

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English	Metric Sobolev spaces. I: Equivalence of definitions	scientific article; zbMATH DE number 7960925

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instance of

scholarly article

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title

Metric Sobolev spaces. I: Equivalence of definitions (English)

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Milan Journal of Mathematics

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publication date

27 December 2024

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zbMATH Keywords

metric measure space

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Sobolev space

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Lipschitz function

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derivation

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divergence

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plan of curves

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barycenter

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modulus

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capacity

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Dirichlet space

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Confromal invariants and function-theoretic null-sets

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A simple proof of reflexivity and separability of N^{1,p} Sobolev spaces

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Sobolev spaces in metric measure spaces: reflexivity and lower semicontinuity of slope

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On the duality between $p$-modulus and probability measures

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Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces

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Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below

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

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Duality properties of metric Sobolev spaces and capacity

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Characterizations of rectifiable metric measure spaces

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Nonlinear potential theory on metric spaces

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Existence and almost uniqueness for $p$-harmonic Green functions on bounded domains in metric spaces

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Q3415147

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Energies with respect to a measure and applications to low dimensional structures

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Differentiability of Lipschitz functions on metric measure spaces

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Q3957682

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Infinitesimal hilbertianity of locally $\mathrm{CAT}(\kappa)$-spaces

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A short proof of the infinitesimal hilbertianity of the weighted Euclidean space

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The $p$-weak gradient depends on $p$

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New characterizations of Sobolev metric spaces

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Absolutely continuous functions with values in a metric space

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An elementary proof of Cheeger's theorem on reflexivity of Newton-Sobolev spaces of functions in metric measure spaces

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Density of Lipschitz functions in energy

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Density of continuous functions in Sobolev spaces with applications to capacity

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Curvewise characterizations of minimal upper gradients and the construction of a Sobolev differential

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Coarea inequality for monotone functions on metric surfaces

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Q5565773

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Density of subalgebras of Lipschitz functions in metric Sobolev spaces and applications to Wasserstein Sobolev spaces

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Extremal length and functional completion

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On the differential structure of metric measure spaces and applications

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Nonsmooth differential geometry– An approach tailored for spaces with Ricci curvature bounded from below

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Independence on $p$ of weak upper gradients on $\mathsf{RCD}$ spaces

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

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Behaviour of the reference measure on $\mathsf{RCD}$ spaces under charts

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Sobolev spaces on an arbitrary metric space

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Sobolev met Poincaré

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Nonsmooth calculus

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Sobolev classes of Banach space-valued functions and quasiconformal mappings

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Sobolev Spaces on Metric Measure Spaces

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On the Dirichlet principle

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Plans on measures and \textit{AM}-modulus

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Abstract and concrete tangent modules on Lipschitz differentiability spaces

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Measurability of equivalence classes and MEC$_p$-property

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Regularity of quasi-minimizers on metric spaces

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Sobolev spaces and harmonic maps for metric space targets

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Q4238869

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Universal infinitesimal Hilbertianity of sub-Riemannian manifolds

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A First Course in Sobolev Spaces

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Infinitesimal Hilbertianity of Weighted Riemannian Manifolds

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Yet another proof of the density in energy of Lipschitz functions

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Characterisation of upper gradients on the weighted Euclidean space and applications

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H = W

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Functions of bounded variation on ``good'' metric spaces

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Vector calculus on weighted reflexive Banach spaces

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Sobolev Spaces in Extended Metric-Measure Spaces

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Derivations and Alberti representations

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Metric currents and Alberti representations

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Newtonian spaces: An extension of Sobolev spaces to metric measure spaces

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On general minimax theorems

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The general class of Wasserstein Sobolev spaces: density of cylinder functions, reflexivity, uniform convexity and Clarkson's inequalities

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A first course on zero-sum repeated games

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Lipschitz algebras and derivations. II: Exterior differentiation

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Identifiers

DOI

10.1007/s00032-024-00407-7

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:6655896