Extensions and traces of functions of bounded variation on metric spaces

DOI10.1016/j.jmaa.2014.10.005zbMath1302.26006arXiv1402.0797OpenAlexW1976001089MaRDI QIDQ465421

Panu Lahti

Publication date: 31 October 2014

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.0797

zbMATH Keywords

bounded variationextensionlocalityjump setboundary traceuniform domain

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Functions of bounded variation, generalizations (26A45)

Related Items (10)

An analog of the Neumann problem for the 1-Laplace equation in the metric setting: existence, boundary regularity, and stability ⋮ Strong \textit{BV}-extension and \(W^{1,1}\)-extension domains ⋮ Neumann \(p\)-Laplacian problems with a reaction term on metric spaces ⋮ A remake of Bourgain-Brezis-Mironescu characterization of Sobolev spaces ⋮ The bounded variation capacity and Sobolev-type inequalities on Dirichlet spaces ⋮ Trace theorems for functions of bounded variation in metric spaces ⋮ Fine properties and a notion of quasicontinuity for BV functions on metric spaces ⋮ Neumann problem for \(p\)-Laplace equation in metric spaces using a variational approach: existence, boundedness, and boundary regularity ⋮ Approximation by uniform domains in doubling quasiconvex metric spaces ⋮ Relaxation and integral representation for functionals of linear growth on metric measure spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Pointwise properties of functions of bounded variation in metric spaces
• Nonlinear potential theory on metric spaces
• Functions of bounded variation on ``good metric spaces
• Poincaré inequalities, uniform domains and extension properties for Newton-Sobolev functions in metric spaces
• Measure density and extendability of Sobolev functions
• Quasiconformal mappings and extendability of functions in Sobolev spaces
• Quasiconformal maps in metric spaces with controlled geometry
• On the structure of finite perimeter sets in step 2 Carnot groups
• Fine properties of sets of finite perimeter in doubling metric measure spaces
• Newtonian spaces: An extension of Sobolev spaces to metric measure spaces
• A note on the extension of BV functions in metric measure spaces
• Lipschitz surfaces, perimeter and trace theorems for BV functions in Carnot-Carathéodory spaces
• Remarks on Lipschitz domains in Carnot groups
• Geometric Properties of Planar BV -Extension Domains
• Sobolev Extensions of Hölder Continuous and Characteristic Functions on Metric Spaces
• Non-doubling Ahlfors measures, perimeter measures, and the characterization of the trace spaces of Sobolev functions in Carnot-Carathéodory spaces

This page was built for publication: Extensions and traces of functions of bounded variation on metric spaces