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arXiv · 1406.6350

The continuity equation on metric measure spaces

Nicola Gigli·Bangxian Han
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Abstract

Aim of this paper is to show that it makes sense to write the continuity equation on a metric measure space $(X,d,m)$ and that absolutely continuous curves $\mu_t$ w.r.t. the distance $W_2$ can be completely characterized as solutions of the continuity equation itself, provided we impose the condition $\mu_t\leq Cm$ for every $t$ and some $C>0$.

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Nicola Gigli, Bangxian Han. 2014-06-24. The continuity equation on metric measure spaces. https://doi.org/10.1007/s0052

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