11 papers
On the equivalence of BV notions in metric measure spaces
Luigi Ambrosio, Enrico Pasqualetto, Nageswari Shanmugalingam
The aim of the paper is to compare in detail several notions of space of functions of bounded variation in metric measure spaces . Informall…
Functions of bounded variation and Lipschitz algebras in metric measure spaces
Enrico Pasqualetto, Giacomo Enrico Sodini
Given a unital algebra of locally Lipschitz functions defined over a metric measure space , we study two associated notions of f…
A categorical perspective on extended metric-topological spaces
Enrico Pasqualetto, Timo Schultz, Janne Taipalus
Motivated by the analysis and geometry of metric-measure structures in infinite dimensions, we study the category of extended metric-topological spaces, along with many of its dist…
A topological characterization of indecomposable sets of finite perimeter
Paolo Bonicatto, Panu Lahti, Enrico Pasqualetto
We prove that a set of finite perimeter is indecomposable if and only if it is, up to a choice of suitable representative, connected in the 1-fine topology. This gives a topologica…
Preduals of metric BV spaces
Enrico Pasqualetto
We study the predual of the space of functions of bounded variation defined over a metric measure space with finite. More specifically…
Metric Sobolev spaces II: dual energies and divergence measures
Luigi Ambrosio, Toni Ikonen, Danka LuÄiÄ +1
This is the second of two works concerning the Sobolev calculus on metric measure spaces and its applications. In this work, we focus on several approaches to vector calculus in th…