%0 Journal Article
%J SIAM J. Math. Anal. 42 (2010) 1179-1217
%D 2010
%T Estimates on path functionals over Wasserstein Spaces
%A Stefano Bianchini
%A Alessio Brancolini
%X In this paper we consider the class a functionals (introduced in [Brancolini, Buttazzo, and Santambrogio, J. Eur. Math. Soc. (JEMS), 8 (2006), pp. 415-434] $\\\\mathcal{G}_{r,p}$ defined on Lipschitz curves $\\\\gamma$ valued in the $p$-Wasserstein space. The problem considered is the following: given a measure $\\\\mu$, give conditions in order to assure the existence of a curve $\\\\gamma$ such that $\\\\gamma(0)=\\\\mu$, $\\\\gamma(1)=\\\\delta_{x_0}$, and $\\\\mathcal{G}_{r,p}(\\\\gamma)<+\\\\infty$. To this end, new estimates on $\\\\mathcal{G}_{r,p}(\\\\mu)$ are given, and a notion of dimension of a measure (called path dimension) is introduced: the path dimension specifies the values of the parameters $(r,p)$ for which the answer to the previous reachability problem is positive. Finally, we compare the path dimension with other known dimensions.
%B SIAM J. Math. Anal. 42 (2010) 1179-1217
%G en_US
%U http://hdl.handle.net/1963/3583
%1 717
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-03-09T09:05:25Z\\nNo. of bitstreams: 1\\nestimates_path_functionals.prerint.pdf: 356623 bytes, checksum: 6bc99a8752ef3aae9d1b91d05e8a2f8e (MD5)
%R 10.1137/100782693