By Haynes R. Miller, Douglas C. Ravenel

Throughout the iciness and spring of 1985 a Workshop in Algebraic Topology was once held on the college of Washington. The path notes by way of Emmanuel Dror Farjoun and by means of Frederick R. Cohen contained during this quantity are conscientiously written graduate point expositions of convinced points of equivariant homotopy idea and classical homotopy thought, respectively. M.E. Mahowald has incorporated the various fabric from his extra papers, symbolize quite a lot of modern homotopy concept: the Kervaire invariant, strong splitting theorems, laptop calculation of volatile homotopy teams, and reviews of L(n), Im J, and the symmetric teams.

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8–9, 965–969, 1991. [10] T. Champion, L. De Pascale, P. Juutinen, The 1-Wasserstein distance: local solutions and existence of optimal transport maps, SIAM J. Math. An. (40), no. 1, 1–20, 2008. [11] C. Jimenez, Optimisation de probl`emes de transport, PhD thesis, Universit´e du Sud-Toulon-Var, 2005. [12] L. Kantorovich, On the transfer of masses. Dokl. Acad. Nauk. USSR, (37), 7–8, 1942. [13] R. J. McCann, A convexity principle for interacting gases. Adv. Math. (128), no. 1, 153–159, 1997. [14] G.

4) For H (t) D t 2 this is a simple Laplace equation, and regularity theory is well known. For H (t) D t p this gives a p 0 -Laplace equation, and here lots of studies have been done as well. 5) which leads to a function H which vanishes on B1 . In particular, the corresponding equation for u is very very degenerate and regularity results are less studied (see [7], both for the equivalence with the Wardrop problem and for some regularity proofs). 3 The urban planning of residents and services A very simplified model that has been proposed for studying the distribution of residents and services in a given urban region passes through the minimization of a total quantity F(μ, ν) concerning two unknown densities μ and ν.

For G, there are other interesting choices among functionals which favor concentration. One of them could be G(ν) D h(jx yj) ν(dx)ν(dy), where h is an increasing function and h(jx yj) stands for the cost of managing the interactions between services located at x and at y. This new choice for G is more concerned with the positions of the services, and not only with the size of each pole. These two choices and other possible models give different interesting results when one looks at the minimizers.