60 research outputs found
FOURTH-ORDER OPERATORS WITH UNBOUNDED COEFFICIENTS
No full textWe prove that operators of the form A=-a(x)(2)Delta (2), with |Da(x)| <= ca(x) (1/2), generate analytic semigroups in L-p(R-N) for 1 < p <= infinity and in C-b(R-N). In particular, we deduce generation results for the operator A := -(1 + |x|(2))(alpha) Delta (2), 0 <= alpha <= 2. Moreover, we characterize the maximal domain of such operators in L-p(R-N) for 1 < p < infinity
Rate of convergence in Trotter's approximation theorem
No full textWe give a quantitative estimate of the convergence in Trotter's approximation theorem on the convergence of iterates of linear operators to an assigned semigroup. An application is given concerning the classical Bernstein operator on the d-dimensional simplex
Kernel estimates for Schrödinger type operators with unbounded coefficients and critical exponents
No full textWe consider
the Schr\"odinger type operator (1+|x|^\alpha)\Delta+c|x|^{\alpha-2}, for \alpha> 2, c2.
Heat kernel estimates of the associated semigroup are obtained using the equivalence between
weighted Nash inequalities and ``weighted'' ultracontractivity of a
symmetric Markov semigroup. Moreover we give estimates of the eigenfunctions of the operator for large values of |x|
Some results on second-order elliptic operators with polynomially growing coefficients in Lp-spaces
No full textIn this paper we study minimal realizations in Lp(RN) of the second order elliptic operator Ab,c:=(1+|x|α)Δ+b|x|α−2x⋅∇−c|x|α−2−|x|β,x∈RN, where N≥3, α∈[0,2), β>0, and b,c are real numbers. We use quadratic form methods to prove that (Ab,c,Cc∞(RN∖{0})) admits an extension that generates an analytic C0-semigroup for all p∈(1,∞). Moreover, we give conditions on the coefficients under which this extension is precisely the closure of (Ab,c,Cc∞(RN∖{0}))
Through-the-needle biopsy of pancreatic cystic lesions: stronger evidences of higher diagnostic yield compared with cytology
No full textNo abstract availabl
Endoscopic ultrasound-guided gallbladder drainage after real-time assessment of cystic duct exclusion following biliary placement of an uncovered metal
No full textBi-Kolmogorov type operators and weighted Rellich’s inequalities
No full textIn 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)
Elliptic operators with unbounded diffusion, drift and potential terms
No full textWe prove that the realization A_p in Lp(R^N), 1 < p < infty , of the elliptic operator
A = (1+|x|^alpha)Delta +b|x|^{alpha -2}x
abla -c|x|^eta with domain D(Ap) = {u in
W^{2,p}(R^N) : Au in Lp(RN)} generates a strongly continuous analytic semigroup
T(t) provided that alpha > 2, eta > alpha - 2 and any constants b in R and c > 0. This
generalizes recent results in in the litterature. Moreover we show that T(t) is
consistent, immediately compact and ultracontractive
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