Displaying similar documents to “Asymptotics of permutations with nearly periodic patterns of rises and falls.”

A two-scale approach to logarithmic Sobolev inequalities and the hydrodynamic limit

Natalie Grunewald, Felix Otto, Cédric Villani, Maria G. Westdickenberg (2009)

Annales de l'I.H.P. Probabilités et statistiques

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We consider the coarse-graining of a lattice system with continuous spin variable. In the first part, two abstract results are established: sufficient conditions for a logarithmic Sobolev inequality with constants independent of the dimension (Theorem 3) and sufficient conditions for convergence to the hydrodynamic limit (Theorem 8). In the second part, we use the abstract results to treat a specific example, namely the Kawasaki dynamics with Ginzburg–Landau-type potential.

Boundedness and compactness of the embedding between spaces with multiweighted derivatives when 1 ≤ q < p < ∞

Zamira Abdikalikova, Ryskul Oinarov, Lars-Erik Persson (2011)

Czechoslovak Mathematical Journal

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We consider a new Sobolev type function space called the space with multiweighted derivatives W p , α ¯ n , where α ¯ = ( α 0 , α 1 , ... , α n ) , α i ∈ ℝ , i = 0 , 1 , ... , n , and ∥ f ∥ W p , α ¯ n = ∥ D α ¯ n f ∥ p + ∑ i = 0 n - 1 | D α ¯ i f ( 1 ) | , D α ¯ 0 f ( t ) = t α 0 f ( t ) , D α ¯ i f ( t ) = t α i d d t D α ¯ i - 1 f ( t ) , i = 1 , 2 , ... , n . We establish necessary and sufficient conditions for the boundedness and compactness of the embedding W p , α ¯ n ↪ W q , β ¯ m , when 1 ≤ q < p < ∞ , 0 ≤ m < n .