1 citations · 2 across the 8 of their papers we have counts for
10 papers
Scale-invariant bounds on thin sets for measures satisfying a first-order PDE and the anisotropic Michael-Simon inequality
Guido De Philippis, Luca Gennaioli, Alessandro Pigati +1
We prove mass estimates for PDE-constrained measures on sets of -finite -measure, assuming an appropriate rank condition. As an application, we derive a Michael-…
Improvement of the dimension bound for unweighted RCD spaces
Camillo Brena, Luca Gennaioli
We show that if is an space for some and , then it is also a (non-collapsed) space. In other words, unw…
Concentration phenomena and the Vanishing Mass Conjecture
Luca Gennaioli, Filip Rindler
Concentrating (that is, non-equi-integrable) sequences of functions satisfying linear PDE constraints arise in a wide variety of problems in PDE, the calculus of variations, and ge…
Lipschitz continuity of harmonic maps between spaces and spaces
Luca Gennaioli
We are going to prove that energy minimizing harmonic maps from a domain inside an whose image lies in a small ball inside a space are locally L…
Sets of finite perimeter on Riemannian manifolds and stochastic completeness
Luca Gennaioli
We prove a heat semigroup characterization of the total variation for compactly supported on arbitrary smooth complete weighted Riemannian manifolds, extending the main…
A new Duhamel-type principle with applications to geometric (in)equalities
Michele Caselli, Luca Gennaioli
We introduce a simple new method, based on the Caffarelli-Silvestre extension and a Duhamel-type formula, to derive exact pointwise identities for fractional commutators and nonlin…
Sharp conditions for the BBM formula and asymptotics of heat content-type energies
Luca Gennaioli, Giorgio Stefani
Given , we provide sufficient and necessary conditions on the non-negative measurable kernels ensuring convergence of the associated Bourgain-Br…
Comments on the regularity of harmonic maps between singular spaces
Luca Gennaioli, Nicola Gigli, Hui-Chun Zhang +1
In this work we are going to establish Hölder continuity of harmonic maps from an open set in an space valued into a space, with the constraint…
Fourier transform of BV functions and applications
Thomas Beretti, Luca Gennaioli
This paper investigates the relation between the Fourier transform of {\rm BV} (bounded variation) functions and their jump sets. We introduce the notion of -jump product and…
Asymptotics as of the fractional perimeter on Riemannian manifolds
Michele Caselli, Luca Gennaioli
In this work we study the asymptotics of the fractional Laplacian as on any complete Riemannian manifold , both of finite and infinite volume. Surprisingly enough…