0000000000342490
AUTHOR
Abdelaziz Rhandi
Kernel estimates for nonautonomous Kolmogorov equations with potential term
Using time dependent Lyapunov functions, we prove pointwise upper bounds for the heat kernels of some nonautonomous Kolmogorov operators with possibly unbounded drift and diffusion coefficients and a possibly unbounded potential term.
Global properties of generalized Ornstein–Uhlenbeck operators on Lp(RN,RN) with more than linearly growing coefficients
AbstractWe show that the realization Ap of the elliptic operator Au=div(Q∇u)+F⋅∇u+Vu in Lp(RN,RN), p∈[1,+∞[, generates a strongly continuous semigroup, and we determine its domain D(Ap)={u∈W2,p(RN,RN):F⋅∇u+Vu∈Lp(RN,RN)} if 1<p<+∞. The diffusion coefficients Q=(qij) are uniformly elliptic and bounded together with their first-order derivatives, the drift coefficients F can grow as |x|log|x|, and V can grow logarithmically. Our approach relies on the Monniaux–Prüss theorem on the sum of noncommuting operators. We also prove Lp–Lq estimates and, under somewhat stronger assumptions, we establish pointwise gradient estimates and smoothing of the semigroup in the spaces Wα,p(RN,RN), α∈[0,1], wher…