Long time behavior of heat kernels of operators with unbounded drift terms

El Maati Ouhabaz (1)

1 IMB - Institut de Mathématiques de Bordeaux

Given a second-order elliptic operator on Rd, with bounded diffusion coefficients and unbounded drift, which is the generator of a strongly continuous semigroup on L2(Rd) represented by an integral, we study the time behavior of the integral kernel and prove estimates on its decay at infinity. If the diffusion coefficients are symmetric, a local lower estimate is also proved.

Mots clés: parabolic operators; unbounded drifts; heat kernels

Domaines: Equations aux dérivées partielles [math.AP]; Analyse fonctionnelle [math.FA]

El Maati Ouhabaz. Long time behavior of heat kernels of operators with unbounded drift terms. Journal of Mathematical Analysis and Applications, 2011, 377, pp.170-179. ⟨10.1016/j.jmaa.2010.10.023⟩. ⟨hal-00998100⟩