Comparisons of relative BV-capacities and Sobolev capacity in metric spaces

DOI10.1016/j.na.2011.05.036zbMath1248.28002arXiv1104.0797OpenAlexW1591460739WikidataQ109994484 ScholiaQ109994484MaRDI QIDQ555074

Heikki Hakkarainen, Nageswari Shanmugalingam

Publication date: 22 July 2011

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1104.0797

zbMATH Keywords

Sobolev spacecapacityfunctions of bounded variationanalysis on metric measure spaces

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Contents, measures, outer measures, capacities (28A12)

Related Items (15)

The variational 1-capacity and BV functions with zero boundary values on doubling metric spaces ⋮ An analog of the Neumann problem for the 1-Laplace equation in the metric setting: existence, boundary regularity, and stability ⋮ The bounded variation capacity and Sobolev-type inequalities on Dirichlet spaces ⋮ Approximation of BV by SBV functions in metric spaces ⋮ Trace theorems for functions of bounded variation in metric spaces ⋮ BV capacity and Sobolev capacity for the Laguerre operator ⋮ Relative isoperimetric inequalities and sufficient conditions for finite perimeter on metric spaces ⋮ Capacity \& perimeter from \(\alpha\)-Hermite bounded variation ⋮ Fine properties and a notion of quasicontinuity for BV functions on metric spaces ⋮ Capacities and 1-strict subsets in metric spaces ⋮ Unnamed Item ⋮ Restriction of heat equation with Newton-Sobolev data on metric measure space ⋮ Notions of Dirichlet problem for functions of least gradient in metric measure spaces ⋮ BV capacity for the Schrödinger operator with an inverse-square potential ⋮ Sobolev and variational capacities in the Hermite setting and their applications

Cites Work

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• Geometric implications of the Poincaré inequality
• Change of variables for absolutely continuous functions
• On some recent developments of the theory of sets of finite perimeter
• Some connections between isoperimetric and Sobolev-type inequalities
• Sobolev met Poincaré
• Lebesgue points and capacities via boxing inequality in metric spaces
• Some fine properties of sets of finite perimeter in Ahlfors regular metric measure spaces
• Regularity of quasi-minimizers on metric spaces
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