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Displaying similar documents to “Harnack inequality and heat kernel estimates for the Schrödinger operator with Hardy potential”

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....

Steady-state buoyancy-driven viscous flow with measure data

Tomáš Roubíček (2001)

Mathematica Bohemica

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Steady-state system of equations for incompressible, possibly non-Newtonean of the p -power type, viscous flow coupled with the heat equation is considered in a smooth bounded domain Ω ⊂ ℝ n , n = 2 or 3, with heat sources allowed to have a natural L 1 -structure and even to be measures. The existence of a distributional solution is shown by a fixed-point technique for sufficiently small data if p > 3 / 2 (for n = 2 ) or if p > 9 / 5 (for n = 3 ).