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Polynomial stability of operator semigroups
No full textWe investigate polynomial decay of classical solutions of linear evolution equations. For bounded strongly continuous semigroups on a Banach space this property is closely related to polynomial growth estimates of the resolvent of the generator. For systems of commuting normal operators polynomial decay is characterized in terms of the location of the generator spectrum. The results are applied to systems of coupled wave-type equations
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
L_p regularity for elliptic operators with unbounded coefficients
No full textIn this paper we prove the generation of positive and analytic semigroups in and for some . Analogous results are also established in the spaces and . The proofs are based essentially on an interpolation inequality between and . As an application we show that the generalized Ornstein-Uhlenbeck operator with domain generates an analytic semigroup on the weighted space , where
L^p-theory for some elliptic and parabolic problems with first order degeneracy at the boundary
No full text
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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