Displaying similar documents to “A simple proof of the logarithmic Sobolev inequality on the circle”

Vortex motion and phase-vortex interaction in dissipative Ginzburg-Landau dynamics

F. Bethuel, G. Orlandi, D. Smets (2004)

Journées Équations aux dérivées partielles

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We discuss the asymptotics of the parabolic Ginzburg-Landau equation in dimension N ≥ 2 . Our only asumption on the initial datum is a natural energy bound. Compared to the case of “well-prepared” initial datum, this induces possible new energy modes which we analyze, and in particular their mutual interaction. The two dimensional case is qualitatively different and requires a separate treatment.

Description of the lack of compactness for the Sobolev imbedding

P. Gérard (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We prove that any bounded sequence in a Hilbert homogeneous Sobolev space has a subsequence which can be decomposed as an almost-orthogonal sum of a sequence going strongly to zero in the corresponding Lebesgue space, and of a superposition of terms obtained from fixed profiles by applying sequences of translations and dilations. This decomposition contains in particular the various versions of the concentration-compactness principle.