1,721,319 research outputs found
The Monge problem for strictly convex norms in R^N
No full textWe prove the existence of an optimal transport map for the Monge problem in a convex bounded subset of Rd under the assumptions that the first marginal is absolutely continuous with respect to the Lebesgue measure and that the cost is given by a strictly convex norm. We propose a new approach which does not use disintegration of measures
Principles of comparison with distance functions for absolute minimizers
No full textWe extend the principle of comparison with cones introduced by Crandall, Evans and Gariepy in [12] for the Minimizing Lipschitz Extension Problem to a wide class of supremal functionals. This gives a geometrical characterization of the absolute minimizers (optimal solutions whose minimality is local). Some application to the stability of absolute minimizers with respect to the Gamma-convergence is given. A variation of the basic idea also allows to characterize the minimal Lipschitz extensions in length metric spaces
Asymptotic behavior of non linear eigenvalue problems involving Laplacian type operators
No full textWe study the asymptotic behaviour of two nonlinear eigenvalue problems which involve p-Laplacian-type operators. In the first problem we consider the limit as p goes to infinity of the sequences of the kth eigenvalues of the p-Laplacian operators. The second problem we study is the homogenization of nonlinear eigenvalue problems for some p-Laplacian-type operators with p fixed. Our asymptotic analysis relies on a convergence result for particular critical values of a class of Rayleigh quotients, stated in a unified framework, and on the notion of Gamma-convergence
The infinite-eigenvalue problem and a problem of optimal transportation
No full textThe so-called eigenvalues and eigenfunctions of the infinite Laplacian ∆∞ are defined through an asymptotic study of that of the usual p-Laplacian ∆p, this brings to a characterization via a non-linear eigenvalue problem for a PDE satisfied in the viscosity sense. In this paper, we obtain an other characterization of the first eigenvalue via a problem of optimal transportation, and recover properties of the first eigenvalue and corresponding positive eigenfunctions
Continuity and estimates for multimarginal optimal transportation problems with singular costs
Full text linkWe consider some repulsive multimarginal optimal transportation problems which include, as a particular case, the Coulomb cost. We prove a regularity property of the minimizers (optimal transportation plan) from which we deduce existence and some basic regularity of a maximizer for the dual problem (Kantorovich potential).
This is then applied to obtain some estimates of the cost and to the study of continuity properties
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Lettres de Henri III, Roi de France, recueillies par Pierre Champion, t. I
No full textBernard-Maitre Henri. Lettres de Henri III, Roi de France, recueillies par Pierre Champion, t. I. In: Revue d'histoire de l'Église de France, tome 46, n°143, 1960. pp. 125-127
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