Uniqueness for elliptic operators on with unbounded coefficients

Lp-uniqueness for elliptic operators with unbounded coefficients inRN

“…Hence, assumptions on the growth at infinity of the coefficients of the operator A more restrictive than in the C b -case are to be prescribed. Typically, the diffusion coefficients are supposed to be bounded or to grow at most slightly more than quadratically at infinity, and some suitable compensation conditions on the coefficients are prescribed (see, e.g., the papers [9][10][11]16,17,23,25,26,28,30,31]). The suitable L p -spaces where to analyze elliptic operators with unbounded coefficients are L p -spaces related to particular measures, the so-called invariant measures and infinitesimally invariant measures.…”

Functional calculus for some perturbations of the Ornstein–Uhlenbeck operator

“…As a consequence of a result of Metafune et al [17], we shall show that if (2.1) holds, then the spectrum of G Φ p is discrete and it does not depend on p. Let {P Φ n } n∈N be the spectral resolution of the identity for which…”

Global Lp estimates for degenerate Ornstein‐Uhlenbeck operators with variable coefficients

“…The considered L p -spaces are defined with respect to Lebesgue measure or with respect to an invariant measure which has also a probabilistic interpretation (see, for instance, [6], [7], [8], [10], [11], [14], [16] and the references therein).…”