BV functions and nonlocal functionals in metric measure spaces

Absolutely continuous real functions of several variables, functions of bounded variation (26B30) Sobolev (and similar kinds of) spaces of functions on metric spaces; analysis on metric spaces (46E36)

Cites Work

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Two subtle convex nonlocal approximations of the BV-norm
The BBM formula revisited
Integral energy characterization of Hajłasz-Sobolev spaces
Non-convex, non-local functionals converging to the total variation
A new approach to Sobolev spaces and connections to \(\Gamma\)-convergence
\(\Gamma\)-convergence, Sobolev norms, and BV functions
Nonlinear potential theory on metric spaces
Characterization of Sobolev and BV spaces
Functions of bounded variation on ``good metric spaces
Quasiconformal maps in metric spaces with controlled geometry
Differentiability of Lipschitz functions on metric measure spaces
On an open question about functions of bounded variation.
Interpolations and fractional Sobolev spaces in Carnot groups
Non-local functionals related to the total variation and connections with image processing
New characterizations of Sobolev metric spaces
Newtonian spaces: An extension of Sobolev spaces to metric measure spaces
Sobolev spaces and harmonic maps for metric space targets
Sobolev spaces revisited
Bourgain-Brezis-Mironescu approach in metric spaces with Euclidean tangents
Non-local, non-convex functionals converging to Sobolev norms
Magnetic BV-functions and the Bourgain-Brezis-Mironescu formula
A distributional approach to fractional Sobolev spaces and fractional variation: existence of blow-up
The Poincaré inequality is an open ended condition
Corrigendum to ``Characterization of Sobolev and \(BV\) spaces
Relaxation and integral representation for functionals of linear growth on metric measure spaces
Nonlocal Operators with Applications to Image Processing
Sobolev met Poincaré
Some characterizations of magnetic Sobolev spaces
Sobolev Spaces on Metric Measure Spaces
Sobolev-type spaces from generalized Poincaré inequalities
A characterization of BV and Sobolev functions via nonlocal functionals in metric spaces
A distributional approach to fractional Sobolev spaces and fractional variation: asymptotics. I
A Bourgain-Brezis-Mironescu-Dávila theorem in Carnot groups of step two
Families of functionals representing Sobolev norms

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