Global properties of generalized Ornstein-Uhlenbeck operators on Lp (RN, RN) with more than linearly growing coefficients

Matthias Georg Hieber, Luca Lorenzi*, Jan Prüss, Abdelaziz Rhandi, Roland Schnaubelt

*この研究の対応する著者

研究成果: Article査読

20 被引用数 (Scopus)

抄録

We show that the realization Ap of the elliptic operator A u = div (Q ∇ u) + F ṡ ∇ u + V u in Lp (RN, RN), p ∈ [1, + ∞ [, generates a strongly continuous semigroup, and we determine its domain D (Ap) = {u ∈ W2, p (RN, RN) : F ṡ ∇ u + V u ∈ Lp (RN, RN)} if 1 < p < + ∞. The diffusion coefficients Q = (qi j) 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 < + ∞.

本文言語English
ページ(範囲)100-121
ページ数22
ジャーナルJournal of Mathematical Analysis and Applications
350
1
DOI
出版ステータスPublished - 2009 2 1
外部発表はい

ASJC Scopus subject areas

  • 分析
  • 応用数学

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