1 citations · 4 across the 12 of their papers we have counts for
4 papers · 1 filter
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…