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**publisher and metadata sources**).Abstract The aim of this note is to generalize to the class of non collapsed RCD(K, N) metric measure spaces the volume bound for the effective singular strata obtained by Cheeger and Naber for non… Continue Reading

We establish new approximation results, in the sense of Lusin, of Sobolev functions by Lipschitz ones, in some classes of non-doubling metric measure structures. Our proof technique relies upon… Continue Reading

The aim of this note is to generalize to the class of non collapsed RCD(K, N) metric measure spaces the volume bound for the effective singular strata obtained by Cheeger and Naber for non collapsed… Continue Reading

We prove a regularity result for Lagrangian flows of Sobolev vector fields over RCD(K,N) metric measure spaces, regularity is understood with respect to a newly defined quasi-metric built from the… Continue Reading

This note is dedicated to the study of the asymptotic behaviour of sets of finite perimeter over \({{\,\mathrm{RCD}\,}}(K,N)\) metric measure spaces. Our main result asserts existence of a Euclidean… Continue Reading

The aim of this note is to prove a sharp regularity estimate for solutions of the continuity equation associated to vector fields of class $W^{1,p}$ with $p>1$. Regularity is understood with respect… Continue Reading

In the last years the study of RCD(K,N) metric measure spaces has undergone a fast development. After the introduction of the curvature-dimension condition CD(K,N) in the independent works [37, 38]… Continue Reading

Abstract Two notions of “having a derivative of logarithmic order” have been studied. They come from the study of regularity of flows and renormalized solutions for the transport and continuity… Continue Reading

The aim of this note is to provide regularity results for Regular Lagrangian flows of Sobolev vector fields over compact metric measure spaces verifying the Riemannian curvature dimension condition.… Continue Reading

This note is devoted to the study of sets of finite perimeter over $\RCD(K,N)$ metric measure spaces. Its aim is to complete the picture about the generalization of De Giorgi's theorem within this… Continue Reading