Displaying similar documents to “Interpolated inequalities between exponential and Gaussian, Orlicz hypercontractivity and isoperimetry.”

A logarithmic Sobolev form of the Li-Yau parabolic inequality.

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...

Mappings of finite distortion: sharp Orlicz-conditions.

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.

Weighted Sobolev-Lieb-Thirring inequalities.

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.

Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates.

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,...

Super and ultracontractive bounds for doubly nonlinear evolution equations.

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...