From the 2 of 5 linked papers with an AI index.
5 papers
Osgood meets Ambrosio-DiPerna-Lions
Guido De Philippis, Leonardo Franchi
The paper extends the Ambrosio‑DiPerna‑Lions theory for transport equations to vector fields that meet an Osgood condition, proving uniqueness and renormalization of bounded…
Regularity estimates in transport equations via heat flow and quantitative differentiation
Elia Brué, Maria Colombo, Guido De Philippis +1
The paper establishes quantitative estimates for commutators in transport equations, showing how logarithmic Sobolev regularity propagates via heat flow and using quantitative diff…
Optimal transport maps, majorization, and log-subharmonic measures
Guido De Philippis, Yair Shenfeld
Caffarelli's contraction theorem bounds the derivative of the optimal transport map between a log-convex measure and a strongly log-concave measure. We show that an analogous pheno…
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(…
Non-collapsed spaces with Ricci curvature bounded from below
Guido De Philippis, Nicola Gigli
We propose a definition of non-collapsed space with Ricci curvature bounded from below and we prove the versions of Colding's volume convergence theorem and of Cheeger-Colding dime…