199 citations · 522 across the 42 of their papers we have counts for
54 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-…
-free measures and the Rank-one Theorem in Carnot Groups
Guido De Philippis, Alberto Gervani, Annalisa Massaccesi +1
We establish a structure theorem for measures satisfying left-invariant PDE constraints in Carnot groups. Our generalization, that takes inspiration from the paper arxiv:1601.06543…
Optimal regularity for vectorial, higher order and non-minimizing Bernoulli problems
Guido De Philippis, Jonas Hirsch, Mickaël Nahon
We prove the Lipschitz regularity of solutions for a wide class of generalized Bernoulli free boundary problems, in vectorial, higher order, and non-minimizing settings. Our method…
Osgood meets Ambrosio-DiPerna-Lions
Guido De Philippis, Leonardo Franchi
In this note we extend the Ambrosio-DiPerna-Lions theory on the well-posedness of the transport equation to the case in which the vector field satisfies an Osgood condition.…
Regularity estimates in transport equations via heat flow and quantitative differentiation
Elia Brué, Maria Colombo, Guido De Philippis +1
The purpose of this note is twofold. First, we prove quantitative estimates for the Ambrosio-Trevisan commutator which implies propagation of logarithmic Sobolev regularity. Second…
Michael-Simon inequality for anisotropic energies close to the area via multilinear Kakeya-type bounds
Guido De Philippis, Alessandro Pigati
Given an anisotropic integrand , we can generalize the classical isotropic area by looking at the functional $$\mathcal{F}(Σ^k):=\int_ΣF(T…