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Variational solutions to the total variation flow on metric measure spaces

Autor: Buffa, Vito, Kinnunen, Juha, Camacho, Cintia Pacchiano

We discuss a purely variational approach to the total variation flow on metric measure spaces with a doubling measure and a Poincar\'e inequality. We apply the concept of parabolic De Giorgi classes together with upper gradients, Newtonian spaces and

Externí odkaz: http://arxiv.org/abs/2109.11908

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

Autor: Buffa, Vito, Collins, Michael, Camacho, Cintia Pacchiano

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 $(\mathcal{X}, d, \mu)$ satisfying a doubling condition and supporting a Poinc

Externí odkaz: http://arxiv.org/abs/2004.09243

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Time-smoothing for parabolic variational problems in metric measure spaces

Autor: Buffa, Vito

In 2013, Masson and Siljander determined a method to prove that the $p$-minimal upper gradient $g_{f_\varepsilon}$ for the time mollification $f_\varepsilon$, $\varepsilon>0$, of a parabolic Newton-Sobolev function $f\in L^p_\mathrm{loc}(0,\tau;N^{1,

Externí odkaz: http://arxiv.org/abs/2002.00093

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Rough traces of $BV$ functions in metric measure spaces

Autor: Buffa, Vito, Miranda Jr, Michele

Publikováno v: Annales Fennici Mathematici, 46(1), 309-333 (2021)

Following a Maz'ya-type approach, we adapt the theory of rough traces of functions of bounded variation ($BV$) in the context of doubling metric measure spaces supporting a Poincar\'e inequality. This eventually allows for an integration by parts for

Externí odkaz: http://arxiv.org/abs/1907.01673

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

Autor: Buffa, Vito, Comi, Giovanni Eugenio, Miranda Jr, Michele

By employing the differential structure recently developed by N. Gigli, we first give a notion of functions of bounded variation ($BV$) in terms of suitable vector fields on a complete and separable metric measure space $(\mathbb{X},d,\mu)$ equipped

Externí odkaz: http://arxiv.org/abs/1906.07432

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