Published Paper
Inserted: 27 sep 2012
Last Updated: 25 jan 2014
Journal: Journal of Mathematical Sciences
Volume: 196
Number: 2
Pages: 152-164
Year: 2014
Doi: 10.1007/s10958-013-1647-4
Notes:
Proceedings of the conference "Monge-Kantorovich optimal transportation problem, transport metrics and their applications" (EIMI, St-Petersburg, June 2012)
Abstract:
We recall some known and present several new results about Sobolev spaces defined with respect to a measure $\mu$, in particular a precise pointwise description of the tangent space to $\mu$ in dimension 1. This allows to obtain an interesting, original compactness result which stays open in $\mathbb{R}^d$, $d>1$, and can be applied to a new transport problem, with gradient penalization.
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