Displaying similar documents to “Initial-boundary value problems for second order systems of partial differential equations∗”

Initial-boundary value problems for second order systems of partial differential equations

Heinz-Otto Kreiss, Omar E. Ortiz, N. Anders Petersson (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previously been made to write a second order system consisting of equations as a larger first order system. Unfortunately, the resulting first order system consists, in general, of more than 2 equations which leads to many complications, such as side conditions which must be satisfied by the solution of the larger...

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.

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].

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.