Displaying similar documents to “Optimal heat kernel bounds under logarithmic Sobolev inequalities”

Heat kernel estimates for critical fractional diffusion operators

Longjie Xie, Xicheng Zhang (2014)

Studia Mathematica

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We construct the heat kernel of the 1/2-order Laplacian perturbed by a first-order gradient term in Hölder spaces and a zero-order potential term in a generalized Kato class, and obtain sharp two-sided estimates as well as a gradient estimate of the heat kernel, where the proof of the lower bound is based on a probabilistic approach.

Large time behaviour of heat kernels on non-compact manifolds: fast and slow decays

Thierry Coulhon (1998)

Journées équations aux dérivées partielles

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In this talk we shall present some joint work with A. Grigory’an. Upper and lower estimates on the rate of decay of the heat kernel on a complete non-compact riemannian manifold have recently been obtained in terms of the geometry at infinity of the manifold, more precisely in terms of a kind of L 2 isoperimetric profile. The main point is to connect the decay of the L 1 - L ∞ norm of the heat semigroup with some adapted Nash or Faber-Krahn inequalities, which is done by functional analytic methods....

Large time behaviour of solutions to nonhomogeneous diffusion equations

Jean Dolbeault, Grzegorz Karch (2006)

Banach Center Publications

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This note is devoted to the study of the long time behaviour of solutions to the heat and the porous medium equations in the presence of an external source term, using entropy methods and self-similar variables. Intermediate asymptotics and convergence results are shown using interpolation inequalities, Gagliardo-Nirenberg-Sobolev inequalities and Csiszár-Kullback type estimates.