1,720,976 research outputs found
Global properties of invariant measures
No full textWe study global regularity properties of invariant measures associated with second order
differential operators in RN. Under suitable conditions, we prove global boundedness of the
density, Sobolev regularity, a Harnack inequality and pointwise upper and lower bounds
Bi-Kolmogorov type operators and weighted Rellich’s inequalities
Full text linkIn this paper we consider the symmetric Kolmogorov operator L=Δ+∇μμ·∇ on L2(RN, dμ) , where μ is the density of a probability measure on RN. Under general conditions on μ we prove first weighted Rellich’s inequalities and deduce that the operators L and - L2 with domain H2(RN, dμ) and H4(RN, dμ) respectively, generate analytic semigroups of contractions on L2(RN, dμ). We observe that dμ is the unique invariant measure for the semigroup generated by - L2 and as a consequence we describe the asymptotic behaviour of such semigroup and obtain some local positivity properties. As an application we study the bi-Ornstein-Uhlenbeck operator and its semigroup on L2(RN, dμ)
On Schroedinger type operators with unbounded coefficients: Generation and heat kernel estimates
No full textWe consider the Schroedinger type operator , for and . We prove that, for any , the minimal realization of operator in generates a strongly continuous analytic semigroup .
For and , we then prove some upper estimates for the heat kernel associated to the semigroup
.
As a consequence we obtain an estimate for large of the eigenfunctions of . Finally, we extend such estimates to a class of divergence type elliptic operators
regularity for elliptic operators with unbounded coefficients
No full textUnder suitable conditions on the functions a, F and V we show that the operator Au = ∇(a∇u) + F · ∇u − V u with domain W^{2,p} intersected with the domai of the potential V
generates a positive analytic semigroup on
Lp, 1 < p < ∞. Analogous results are also established in the spaces
L1 and C0. As an application we show that the generalized
Ornstein–Uhlenbeck operator AΦ,Gu = Δu − ∇Φ · ∇u + G · ∇u with
domain W2,p(RN, μ) generates an analytic semigroup on the weighted
space Lp(RN, μ), where 1 < p < ∞ and μ(dx) = e
−Φ(x)dx
Generation results for vector-valued elliptic operators with unbounded coefficients in Lp spaces
No full textWe consider a class of vector-valued elliptic operators with unbounded coefficients, coupled up to the first order, in the Lebesgue space Lp(Rd; Rm) with p∈ (1 , ∞). Sufficient conditions to prove generation results of an analytic C-semigroup T(t) , together with a characterization of the domain of its generator, are given. Some results related to the hypercontractivity and the ultraboundedness of the semigroup are also established
On vector-valued Schrödinger operators with unbounded diffusion in Lp spaces
Full text linkWe prove generation results of analytic strongly continuous semigroups on Lp(Rd, Rm) (1 < p< ∞) for a class of vector-valued Schrödinger operators with unbounded coefficients. We also prove Gaussian type estimates for such semigroups
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