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papers

Publications (5)

math.AP2022

Variational solutions to the total variation flow on metric measure spaces

Vito Buffa, Juha Kinnunen, Cintia Pacchiano Camacho

We discuss a purely variational approach to the total variation flow on metric measure spaces with a doubling measure and a PoincarÃ© inequality. We apply the concept of parabolic…

math.AP2022

Time-smoothing for parabolic variational problems in metric measure spaces

Vito Buffa

In 2013, Masson and Siljander determined a method to prove that the $p$ -minimal upper gradient $g_{f_{ε}}$ for the time mollification $f_{ε}$ , $ε > 0$ , of a…

math.DG2021

On $B V$ functions and essentially bounded divergence-measure fields in metric spaces

Vito Buffa, Giovanni Eugenio Comi, Michele Miranda

By employing the differential structure recently developed by N. Gigli, we first give a notion of functions of bounded variation ( $B V$ ) in terms of suitable vector fields on a comp…

math.AP2021

Existence of parabolic minimizers to the total variation flow on metric measure spaces

Vito Buffa, Michael Collins, Cintia Pacchiano Camacho

We give an existence proof for variational solutions $u$ associated to the total variation flow. Here, the functions being considered are defined on a metric measure space $(\mathc…

math.MG2021

Rough traces of $B V$ functions in metric measure spaces

Vito Buffa, Michele Miranda

Following a Maz'ya-type approach, we adapt the theory of rough traces of functions of bounded variation ( $B V$ ) in the context of doubling metric measure spaces supporting a Poincar…