We discuss the problem of the regularity-in-time of the map $t\mapsto T_t\in L^p(\R^d,\R^d;\sigma)$, where $T_t$ is a transport map (optimal or not) from a reference measure $\sigma$ to a measure $\mu_t$ which lies along an absolutely continuous curve $t\mapsto\mu_t$ in the space $P_p(\R^d),W_p$. We prove that in most cases such a map is no more than 1/p-Holder continuous.
On Holder continuity in time of the optimal transport map towards measures along a curve / Gigli, Nicola. - In: PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY. - ISSN 0013-0915. - 54:2(2011), pp. 401-409. [10.1017/S001309150800117X]
On Holder continuity in time of the optimal transport map towards measures along a curve.
Gigli, Nicola
2011-01-01
Abstract
We discuss the problem of the regularity-in-time of the map $t\mapsto T_t\in L^p(\R^d,\R^d;\sigma)$, where $T_t$ is a transport map (optimal or not) from a reference measure $\sigma$ to a measure $\mu_t$ which lies along an absolutely continuous curve $t\mapsto\mu_t$ in the space $P_p(\R^d),W_p$. We prove that in most cases such a map is no more than 1/p-Holder continuous.File in questo prodotto:
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