## Global regularity for solutions to Monge-Ampère type equations

### Description

The optimal transportation problem was formulated by Monge in 1781: given two domains $\Omega, \Omega^* \subset \R^n$ and two mass distributions $f\in L^1(\Omega)$ and $g\in L^1(\Omega^*)$ of the same mass, find the optimal volume-preserving map $T$ between them, where optimality is measured against a cost functional $$\mathcal C(s)=\int_\Omega f(x) c(x,s(x)).$$ %One views the first set $\Omega$ as being filled with mass, %and $c(x,y)$ as being the cost for transporting per unit mass from \$x...[Show more]

Collections Open Access Theses 2018 Thesis (PhD) http://hdl.handle.net/1885/190323 10.25911/5def6669e53c6