## 4 Citations

### Discrete convolutions of BV functions in quasiopen sets in metric spaces

- Mathematics
- 2018

We study fine potential theory and in particular partitions of unity in quasiopen sets in the case $p=1$. Using these, we develop an analog of the discrete convolution technique in quasiopen (instead…

### Traces of Newtonian-Sobolev, Hajlasz-Sobolev, and BV functions on metric spaces

- MathematicsANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
- 2021

We study the boundary traces of Newton-Sobolev, Hajlasz-Sobolev, and BV (bounded variation) functions. Assuming less regularity of the domain than is usually done in the literature, we show that all…

### Discrete convolutions of $$\mathrm {BV}$$BV functions in quasiopen sets in metric spaces

- Mathematics
- 2020

We study fine potential theory and in particular partitions of unity in quasiopen sets in the case $$p=1$$p=1. Using these, we develop an analog of the discrete convolution technique in quasiopen…

## References

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- Mathematics
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We study pointwise properties of functions of bounded variation on a metric space equipped with a doubling measure and a Poincaré inequality. In particular, we obtain a Lebesgue type result for…

### A Notion of Fine Continuity for BV Functions on Metric Spaces

- Mathematics
- 2015

In the setting of a metric space equipped with a doubling measure supporting a Poincaré inequality, we show that BV functions are, in the sense of multiple limits, continuous with respect to a 1-fine…

### Strong approximation of sets of finite perimeter in metric spaces

- Mathematics
- 2016

In the setting of a metric space equipped with a doubling measure that supports a Poincaré inequality, we show that any set of finite perimeter can be approximated in the $$\mathrm {BV}$$BV norm by a…

### The BV-capacity in metric spaces

- Mathematics
- 2010

We study basic properties of the BV-capacity and Sobolev capacity of order one in a complete metric space equipped with a doubling measure and supporting a weak Poincaré inequality. In particular, we…

### Quasicontinuity of Newton-Sobolev functions and density of Lipschitz functions on metric spaces

- Mathematics
- 2008

We show that on complete doubling metric measure spaces X supporting a Poincare inequality, all Newton-Sobolev functions u are quasicontinuous, i.e. that for every a>0 there is an open subset U of X…

### Quasiopen Sets, Bounded Variation and Lower Semicontinuity in Metric Spaces

- MathematicsPotential Analysis
- 2018

In the setting of a complete metric space that is equipped with a doubling measure and supports a Poincaré inequality, we show that the total variation of functions of bounded variation is lower…

### The variational 1-capacity and BV functions with zero boundary values on doubling metric spaces

- MathematicsAdvances in Calculus of Variations
- 2018

Abstract In the setting of a metric space that is equipped with a doubling measure and supports a Poincaré inequality, we define and study a class of BV{\mathrm{BV}} functions with zero boundary…

### Integral representation results for functionals defined on SBV(?; Rm)

- Mathematics
- 1996

We show that lower semicontinuous functionals defined on De Giorgi and Ambrosio’s space of special functions of bounded variation admit an integral representation with Carathéodory integrands, under…

### Lebesgue points and capacities via the boxing inequality in metric spaces

- Mathematics
- 2008

The purpose of this work is to study regularity of Sobolev functions on metric measure spaces equipped with a doubling measure and supporting a weak Poincare inequality. We show that every Sobolev…