Memoirs of the American Mathematical Society 1999; 66 pp; softcover Volume: 137 ISBN10: 0821809385 ISBN13: 9780821809389 List Price: US$43 Individual Members: US$25.80 Institutional Members: US$34.40 Order Code: MEMO/137/653
 In this volume, the authors demonstrate under some assumptions on \(f^+\), \(f^\) that a solution to the classical MongeKantorovich problem of optimally rearranging the measure \(\mu{^+}=f^+dx\) onto \(\mu^=f^dy\) can be constructed by studying the \(p\)Laplacian equation \( \mathrm{div}(\vert DU_p\vert^{p2}Du_p)=f^+f^\) 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 \(f^\). Readership Graduate students and research mathematicians working in optimal control problems involving ODEs. Table of Contents  Introduction
 Uniform estimates on the \(p\)Laplacian, limits as \(p\to\infty\)
 The transport set and transport rays
 Differentiability and smoothness properties of the potential
 Generic properties of transport rays
 Behavior of the transport density along rays
 Vanishing of the transport density at the ends of rays
 Approximate mass transfer plans
 Passage to limits a.e.
 Optimality
 Appendix: Approximating semiconcave and semiconvex functions by \(C^2\) functions
 Bibliography
