Differential Equations Methods for the Monge-Kantorovich Mass Transfer Problem (Memoirs of the AMS) (Memoirs of the American Mathematical Society) - Softcover

Evans, Lawrence C.; Gangbo, Wilfrid

Softcover

ISBN 10: 0821809385 ISBN 13: 9780821809389

Publisher: American Mathematical Society, 1999

Synopsis

In this volume, the authors demonstrate under some assumptions on $f^+$, $f^-$ that a solution to the classical Monge-Kantorovich problem of optimally rearranging the measure $\mu{^+}=f^+dx$ onto $\mu^-=f^-dy$ can be constructed by studying the $p$-Laplacian equation $- \mathrm {div}(\vert DU_p\vert^{p-2}Du_p)=f^+-f^-$ in the limit as $p\rightarrow\infty$. The idea is to show $u_p\rightarrow u$, where $u$ satisfies $\vert Du\vert\leq 1,-\mathrm {div}(aDu)=f^+-f^-$ for some density $a\geq0$, and then to build a flow by solving a nonautonomous ODE involving $a, Du, f^+$ and $f^-$.

Edition details

• Publisher: American Mathematical Society
• Publication date: 1999
• Language: English
• ISBN 10: 0821809385
• ISBN 13: 9780821809389
• Binding: Paperback
• Number of pages: 66