ENGLISH

Differential equations methods for the Monge-Kantorevich mass transfer problem

By Lawrence C. Evans , Wilfrid Gangbo

Book information

Publisher
American Mathematical Society
Year
1999
ISBN
0821809385, 9780821809389
ISSN
0065-9266
LCC
QA3 .A57 no. 653,QA402.6 .A57 no. 653
Open Library ID
OL383201M
Language
english
Format
DJVU
Filesize
954 kB (976570 bytes)
Series
Memoirs of the American Mathematical Society 653
Pages
70\70
Time added
2010-06-26 00:49:36

Description

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 $f^-$.

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