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Optimal heat kernel bounds under logarithmic Sobolev inequalities. (English) Zbl 0898.58052

Author’s abstract: “We establish optimal uniform upper estimates on heat kernels whose generators satisfy a logarithmic Sobolev inequality (or entropy-energy inequality) with the optimal constant of \(\mathbb{R}^n\). Off-diagonals estimates may also be obtained with, however, a smaller distance involving harmonic functions. In the last part, we apply these methods to study some heat kernel decays for diffusion operators on \(\mathbb{R}^n\) of the type \(\Delta- \nabla \cdot\nabla U\) for smooth potential \(U\) with a given growth at infinity”.

MSC:

58J35 Heat and other parabolic equation methods for PDEs on manifolds
58J65 Diffusion processes and stochastic analysis on manifolds
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References:

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