Alessio Figalli
Published 2018-05-13Version 1
To generalize the notion of distribution function to dimension $d\geq 2$, in the recent papers it was proposed a concept of center-outward distribution function based on optimal transportation ideas, and the inferential properties of the corresponding center-outward quantile function were studied. A crucial tool needed to derive the desired inferential properties is the continuity and invertibility for the center-outward quantile function outside the origin, as this ensures the existence of closed and nested quantile contours. The aim of this paper is to prove such a continuity and invertibility result.
Continuity of solutions of a class of fractional equations
Continuity of Selected Pullback Attractors
On the continuity of solutions to the anisotropic $N$-Laplacian with $L^1$ lower order term
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