Abstract
This paper is concerned with some properties of the generalized Ornstein-Uhlenbeck operator
-A(Phi,G) + nu V := -Delta + del Phi center dot del - G center dot del + nu V,
with nonnegative singular potential nu V (x) in the weighted space L-p (R-N, mu), 1 < p < infinity, where mu(dx) = e (-Phi)(x) dx. Sufficient conditions ensuring the m-accretivity, m-sectoriality and m-dispersivity of -A(Phi,G) + nu V in L-p (R-N, mu) are presented. Particularly, it is shown that A(Phi,G) - nu V with a suitable domain is the generator of a quasi-contractive and positivity preserving analytic C-0-semigroup in L-p (R-N, mu). Further, generation of quasi-contractive analytic semigroups by A(Phi,G) - (nu + k)V in L-p(R-N, mu), for some nu > 0 and k is an element of C, is proven. The results improve and complete the recent results established in Metafune et al. (Adv Differ Equ 10(10): 1131-1164, 2005) when V equivalent to 0 and Kojima and Yokota (J Math Anal Appl 364(2): 618-629, 2010) and Sobajima and Yokota (J Math Anal Appl 403(2): 606-618, 2013) when 0 <= V is an element of C-1 (RN). Some examples where our results can be applied are provided, including Kolmogorov operators and operators with polynomially growing drift term.