Displaying similar documents to “A generalized dual maximizer for the Monge–Kantorovich transport problem∗”

A generalized dual maximizer for the Monge–Kantorovich transport problem

Mathias Beiglböck, Christian Léonard, Walter Schachermayer (2012)

ESAIM: Probability and Statistics

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The dual attainment of the Monge–Kantorovich transport problem is analyzed in a general setting. The spaces are assumed to be polish and equipped with Borel probability measures and . The transport cost function :  ×  →  [0,∞]  is assumed to be Borel measurable. We show that a dual optimizer always exists, provided we interpret it as a projective limit of certain finitely additive measures. Our methods are functional analytic and rely on Fenchel’s perturbation technique.

Local semiconvexity of Kantorovich potentials on non-compact manifolds

Alessio Figalli, Nicola Gigli (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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We prove that any Kantorovich potential for the cost function = /2 on a Riemannian manifold (, ) is locally semiconvex in the “region of interest”, without any compactness assumption on , nor any assumption on its curvature. Such a region of interest is of full -measure as soon as the starting measure does not charge – 1-dimensional rectifiable sets.

High-frequency limit of the Maxwell-Landau-Lifshitz equations in the diffractive optics regime

LU Yong (2012)

ESAIM: Proceedings

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We study the Maxwell-Landau-Lifshitz system for highly oscillating initial data, with characteristic frequencies (1  ) and amplitude (1), over long time intervals (1  ), in the limit  → 0. We show that a nonlinear Schrödinger equation gives a good approximation for the envelope of the solution in the time interval under consideration. This extends previous results of Colin and Lannes [1]. This text is a short version of the article [5].

Transition de dépiégeage élastique de vortex supraconducteurs

Enrick Olive, Nicolas Di Scala, Yves Lansac, Yaouen Fily, Jean-Claude Soret (2012)

ESAIM: Proceedings

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We present 2D numerical simulation results of superconductor vortex lattices driven over a random disorder. The vortex dynamics at the depinning threshold is studied at zero temperature in the case of weak disorder. The dynamics is elastic and the depinning transition is analysed in the framework of a second order phase transition where the velocity response to the driving force behaves like  ~ ( −  ...

Square-root rule of two-dimensional bandwidth problem

Lan Lin, Yixun Lin (2012)

RAIRO - Theoretical Informatics and Applications

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The bandwidth minimization problem is of significance in network communication and related areas. Let be a graph of vertices. The two-dimensional bandwidth () of is the minimum value of the maximum distance between adjacent vertices when is embedded into an  ×  grid in the plane. As a discrete optimization problem, determining () is NP-hard in general. However, exact results for this parameter can be derived for some special classes of graphs. This...

Cramér type moderate deviations for Studentized U-statistics

Tze Leng Lai, Qi-Man Shao, Qiying Wang (2012)

ESAIM: Probability and Statistics

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Let be a Studentized U-statistic. It is proved that a Cramér type moderate deviation ( ≥ )/(1 − Φ()) → 1 holds uniformly in [0, ( )) when the kernel satisfies some regular conditions.