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Item Details
| Title:
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DIFFERENTIAL EQUATIONS METHODS FOR THE MONGE-KANTOROVICH MASS TRANSFER PROBLEM
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| By: |
Lawrence C. Evans, Wilfrid Gangbo |
| Format: |
Paperback |
| List price:
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£45.50 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
0821809385 |
| ISBN 13: |
9780821809389 |
| Publisher: |
AMERICAN MATHEMATICAL SOCIETY |
| Pub. date: |
1 January, 1999 |
| Series: |
Memoirs of the American Mathematical Society No. 653 |
| Pages: |
66 |
| Description: |
Demonstrates 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 $p\rightarrow\infty$. |
| 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 $f^-$. |
| Publication: |
US |
| Imprint: |
American Mathematical Society |
| Returns: |
Returnable |
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