32 citations · 52 across the 18 of their papers we have counts for
5 papers · 1 filter
Boundary regularity and stability for spaces with Ricci bounded below
Elia Bruè, Aaron Naber, Daniele Semola
This paper studies the structure and stability of boundaries in noncollapsed spaces, that is, metric-measure spaces with lower Ricc…
A distributional approach to fractional Sobolev spaces and fractional variation: asymptotics II
Elia Bruè, Mattia Calzi, Giovanni E. Comi +1
We continue the study of the space of functions with bounded fractional variation in and of the distributional fractional Sobolev space $S^{α,p}(\…
Advection diffusion equations with Sobolev velocity field
Elia Bruè, Quoc-Hung Nguyen
In this note we study advection diffusion equations associated to incompressible velocity fields with . We present new estimates on the energy dissipation rate and w…
Positive solutions of transport equations and classical nonuniqueness of characteristic curves
Elia Bruè, Maria Colombo, Camillo De Lellis
The seminal work of DiPerna and Lions [Invent. Math., 98, 1989] guarantees the existence and uniqueness of regular Lagrangian flows for Sobolev vector fields. The latter is a suita…
Rectifiability of RCD(K,N) spaces via -splitting maps
Elia Bruè, Enrico Pasqualetto, Daniele Semola
In this note we give new proofs of rectifiability of RCD(K,N) spaces as metric measure spaces and lower semicontinuity of the essential dimension, via -splitting maps. The argum…