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• W1975331471 abstract "We 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<+∞." @default.
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• W1975331471 date "2009-02-01" @default.
• W1975331471 modified "2023-10-16" @default.
• W1975331471 title "Global properties of generalized Ornstein–Uhlenbeck operators on<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif overflow=scroll><mml:msup><mml:mi>L</mml:mi><mml:mi>p</mml:mi></mml:msup><mml:mo stretchy=false>(</mml:mo><mml:msup><mml:mi mathvariant=double-struck>R</mml:mi><mml:mi>N</mml:mi></mml:msup><mml:mo>,</mml:mo><mml:msup><mml:mi mathvariant=double-struck>R</mml:mi><mml:mi>N</mml:mi></mml:msup><mml:mo stretchy=false>)</mml:mo></mml:math>with more than …" @default.
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• W1975331471 doi "https://doi.org/10.1016/j.jmaa.2008.09.011" @default.
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