Differential equations methods for the Monge-Kantorovich mass transfer problem L.C. Evans, W. Gangbo. Memoirs of the American Mathematical Society 653.

Evans, Lawrence C.:

ISBN 10: 0821809385 / ISBN 13: 9780821809389

Published by Providence R.I., American Mathematical Society [1999]., 1999

About this Item

Ex-library with stamp and library-signature. GOOD condition, some traces of use. Ancien Exemplaire de bibliothèque avec signature et cachet. BON état, quelques traces d'usure. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. 49 EVA 9780821809389 Sprache: Englisch Gewicht in Gramm: 550.

Seller Inventory # 2499821

Bibliographic Details

• Title: Differential equations methods for the Monge-Kantorovich mass transfer problem L.C. Evans, W. Gangbo. Memoirs of the American Mathematical Society 653.
• Publisher: Providence R.I., American Mathematical Society [1999].
• Publication Date: 1999
• Language: English
• ISBN 10: 0821809385
• ISBN 13: 9780821809389
• Binding: Softcover
• Weight: 550 grams
• Seller catalogs:
  • SA MATHEMATIK

About this title

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 $f^-$.