Optimal Orlicz-Sobolev embeddings.
Andrea Cianchi (2004)
Revista Matemática Iberoamericana
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Andrea Cianchi (2004)
Revista Matemática Iberoamericana
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Dominique Bakry, Michel Ledoux (2006)
Revista Matemática Iberoamericana
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We present a finite dimensional version of the logarithmic Sobolev inequality for heat kernel measures of non-negatively curved diffusion operators that contains and improves upon the Li-Yau parabolic inequality. This new inequality is of interest already in Euclidean space for the standard Gaussian measure. The result may also be seen as an extended version of the semigroup commutation properties under curvature conditions. It may be applied to reach optimal Euclidean logarithmic Sobolev...
Janne Kauhanen, Pekka Koskela, Jan Malý, Jani Onninen, Xiao Zhong (2003)
Revista Matemática Iberoamericana
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We establish continuity, openness and discreteness, and the condition (N) for mappings of finite distortion under minimal integrability assumptions on the distortion.
R. Tessera (2008)
Revista Matemática Iberoamericana
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I. Gentil, A. Guillin, L. Miclo (2007)
Revista Matemática Iberoamericana
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Kazuya Tachizawa (2005)
Revista Matemática Iberoamericana
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We give a weighted version of the Sobolev-Lieb-Thirring inequality for suborthonormal functions. In the proof of our result we use phi-transform of Frazier-Jawerth.
P. Hajlasz, P. Koskela, H. Tuominen (2008)
Revista Matemática Iberoamericana
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José A. Carrillo, Robert J. McCann, Cédric Villani (2003)
Revista Matemática Iberoamericana
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The long-time asymptotics of certain nonlinear , nonlocal, diffusive equations with a gradient flow structure are analyzed. In particular, a result of Benedetto, Caglioti, Carrillo and Pulvirenti [4] guaranteeing eventual relaxation to equilibrium velocities in a spatially homogencous model of granular flow is extended and quantified by computing explicit relaxation rates. Our arguments rely on establishing generalizations of logarithmic Sobolev inequalities and mass transportation inequalities,...
P. A. Hästo (2007)
Revista Matemática Iberoamericana
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Matteo Bonforte, Gabriele Grillo (2006)
Revista Matemática Iberoamericana
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We use logarithmic Sobolev inequalities involving the p-energy functional recently derived in [15], [21] to prove L-L smoothing and decay properties, of supercontractive and ultracontractive type, for the semigroups associated to doubly nonlinear evolution equations of the form u = Δ(u) (with m(p - 1) ≥ 1) in an arbitrary euclidean domain, homogeneous Dirichlet boundary conditions being assumed. The bound are of the form ||u(t)|| ≤ C||u|| / t for any r ≤ q ∈ [1,+∞) and...