14 citations · 16 across the 10 of their papers we have counts for
6 papers · 1 filter
Metric Sobolev spaces I: equivalence of definitions
Luigi Ambrosio, Toni Ikonen, Danka Lučić +1
This is the first of two works concerning the Sobolev calculus on metric measure spaces and its applications. In this work, we focus on several notions of metric Sobolev space and…
Yet another proof of the density in energy of Lipschitz functions
Danka Lučić, Enrico Pasqualetto
We provide a new, short proof of the density in energy of Lipschitz functions into the metric Sobolev space defined by using plans with barycenter (and thus, a fortiori, into the N…
An axiomatic theory of normed modules via Riesz spaces
Danka Lučić, Enrico Pasqualetto
We introduce and study an axiomatic theory of -normed -modules, where is a Riesz space and is an -algebra; the spaces and also have some additional structu…
Duals and pullbacks of normed modules
Nicola Gigli, Danka Lučić, Enrico Pasqualetto
We give a general description of the dual of the pullback of a normed module. Ours is the natural generalization to the context of modules of the well-known fact that the dual of t…
The metric-valued Lebesgue differentiation theorem in measure spaces and its applications
Danka Lučić, Enrico Pasqualetto
We prove a version of the Lebesgue Differentiation Theorem for mappings that are defined on a measure space and take values into a metric space, with respect to the differentiation…
Characterisation of upper gradients on the weighted Euclidean space and applications
Danka Lučić, Enrico Pasqualetto, Tapio Rajala
In the context of Euclidean spaces equipped with an arbitrary Radon measure, we prove the equivalence among several different notions of Sobolev space present in the literature and…