6533b826fe1ef96bd128398b
RESEARCH PRODUCT
Global properties of generalized Ornstein–Uhlenbeck operators on Lp(RN,RN) with more than linearly growing coefficients
M HieberL LorenziJ PrussAbdelaziz RhandiR. Schnaubeltsubject
Systems of elliptic PDEsUnbounded coefficientsLp-Lq– estimates Gradient Lp-estimatesStrongly continuous semigroupsLp–Lq estimatesGradient Lp-estimatesSystems of elliptic PDEs Unbounded coefficients Strongly continuous semigroups Lp-Lq– estimates Gradient Lp-estimatesdescription
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], where 1<p<+∞.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2009-01-01 | Journal of Mathematical Analysis and Applications |