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Differential Equations Methods for the Monge-Kantorovich Mass Transfer Problem
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Differential Equations Methods for the Monge-Kantorovich Mass Transfer Problem (Paperback)

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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 $f^-$.

Science & MathematicsMathematicsCalculus & mathematical analysisDifferential calculus & equations Publisher: American Mathematical Society Publication Date: 15/01/1999 ISBN-13: 9780821809389  Details: Type: Paperback Format: Books
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