Functions of bounded variation and curves in metric measure spaces
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Publication:323091
DOI10.1515/acv-2014-0045zbMath1360.26010OpenAlexW2525217378MaRDI QIDQ323091
Publication date: 7 October 2016
Published in: Advances in Calculus of Variations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1515/acv-2014-0045
Absolutely continuous real functions of several variables, functions of bounded variation (26B30) Functions of bounded variation, generalizations (26A45)
Related Items (8)
Plans on measures and \textit{AM}-modulus ⋮ 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 \(\mathbb{R}^n\) ⋮ On master test plans for the space of BV functions ⋮ AM‐modulus and Hausdorff measure of codimension one in metric measure spaces ⋮ A version of Stokes's theorem using test curves ⋮ An alternative capacity in metric measure spaces ⋮ The space of functions of bounded variation on curves in metric measure spaces
Cites Work
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- Nonlinear potential theory on metric spaces
- Semmes family of curves and a characterization of functions of bounded variation in terms of curves
- Extremal length and functional completion
- Functions of bounded variation on ``good metric spaces
- Lectures on analysis on metric 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
- Lectures on \(n\)-dimensional quasiconformal mappings
- Sobolev spaces in metric measure spaces: reflexivity and lower semicontinuity of slope
- The $p$-weak gradient depends on $p$
- Lebesgue points and capacities via boxing inequality in metric spaces
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