14 citations · 16 across the 10 of their papers we have counts for
15 papers
Closed BV-extension and -extension sets
Emanuele Caputo, Jesse Koivu, Danka Lučić +1
This paper studies the relations between extendability of different classes of Sobolev and functions from closed sets in general metric measure spaces. Under the ass…
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…
Mass optimization problem with convex cost
Giuseppe Buttazzo, Maria Stella Gelli, Danka Lučić
In this paper we consider a mass optimization problem in the case of scalar state function, where instead of imposing a constraint on the total mass of the competitors, we penalize…
Non-Hilbertian tangents to Hilbertian spaces
Danka Lučić, Enrico Pasqualetto, Tapio Rajala
We provide examples of infinitesimally Hilbertian, rectifiable, Ahlfors regular metric measure spaces having pmGH-tangents that are not infinitesimally Hilbertian.
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…
Gamma-convergence of Cheeger energies with respect to increasing distances
Danka Lučić, Enrico Pasqualetto
We prove a -convergence result for Cheeger energies along sequences of metric measure spaces, where the measure space is kept fixed, while distances are monotonically converging…
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…
Dimension estimates for the boundary of planar Sobolev extension domains
Danka Lučić, Tapio Rajala, Jyrki Takanen
We prove an asymptotically sharp dimension upper-bound for the boundary of bounded simply-connected planar Sobolev -extension domains via the weak mean porosity of the bou…
Universal infinitesimal Hilbertianity of sub-Riemannian manifolds
Enrico Le Donne, Danka Lučić, Enrico Pasqualetto
We prove that sub-Riemannian manifolds are infinitesimally Hilbertian (i.e., the associated Sobolev space is Hilbert) when equipped with an arbitrary Radon measure. The result foll…
Infinitesimal Hilbertianity of weighted Riemannian manifolds
Danka Lučić, Enrico Pasqualetto
The main result of this paper is the following: any `weighted' Riemannian manifold - i.e. endowed with a generic non-negative Radon measure - is `infinitesimally Hilb…
The Serre-Swan theorem for normed modules
Danka Lučić, Enrico Pasqualetto
The aim of this note is to analyse the structure of the -normed -modules over a metric measure space. These are a tool that has been introduced by N. Gigli to develop a d…
Heterogeneous elastic plates with in-plane modulation of the target curvature and applications to thin gel sheets
Virginia Agostiniani, Alessandro Lucantonio, Danka Lučić
We rigorously derive a Kirchhoff plate theory, via -convergence, from a three-di\-men\-sio\-nal model that describes the finite elasticity of an elastically heterogeneous, thin…