1,720,982 research outputs found
Lp-Lq estimates for transition semigroups associated to dissipative stochastic systems
No full textIn a separable Hilbert space, we study supercontractivity and ultracontractivity properties for a transition semigroup associated with a stochastic partial differential equation. This is done in terms of exponential integrability of Lipschitz functions and some logarithmic Sobolev-type inequalities with respect to invariant measures. The abstract characterization results concerning the improvement of summability can be applied to transition semigroups associated to stochastic reaction-diffusion equations. (c) 2025 The Author(s). Published by Elsevier Masson SAS. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)
On coupled systems of PDEs with unbounded coefficients
Full text linkWe study the Cauchy problem associated with parabolic systems of the form Dtu = A(t)u in Cb (Rd; Rm), the space of continuous and bounded functions f: Rd → Rm. Here A(t) is a coupled nonautonomous elliptic operator acting on vector-valued functions, having diffusion and drift coefficients which change from equation to equation. We prove existence and uniqueness of the evolution operator G(t, s) which governs the problem in Cb (Rd; Rm) and its positivity. The compactness of G(t, s) inCb (Rd; Rm) and some of its consequences are also studied. Finally, we extend the evolution operator G(t, s) to the Lp-spaces related to the so called “evolution system of measures” and we provide conditions for the compactness of G(t, s) in this setting
Harnack inequalities with power p is an element of (1,+infinity) for transition semigroups in Hilbert spaces
No full textWe consider the stochastic differential equation{dX(t) = [AX(t) + F(X(t))]dt + C-1/2 dW(t), t > 0,X(0) = x is an element of X,where X is a separable Hilbert space, {W(t)}(t >= 0) is a X-cylindrical Wiener process, A and C are suitable operators on X and F : Dom(F)subset of X -> X is a smooth enough function. We establish a Harnack inequality with power p is an element of(1,+infinity) for the transition semigroup {P(t)}(t >= 0) associated with the stochastic problem above, under less restrictive conditions than those considered in the literature. Some applications to these inequalities are shown
Generation of semigroups associated to strongly coupled elliptic operators in Lp(Rd;Rm)
Full text linkA class of vector-valued elliptic operators with unbounded coefficients, coupled up to the second-order is investigated in the Lebesgue space Lp (Rd ; Rm ) with p ∈ (1, ∞), providing sufficient conditions for the generation of an analytic C0-semigroup T (t). Under further assumptions, a characterization of the domain of the infinitesimal generator is given
Parabolic equations in with general boundary conditions via duality methods
No full textGiven an open domain (possibly unbounded) Omega aS,R (n) , we prove that uniformly elliptic second order differential operators, under nontangential boundary conditions, generate analytic semigroups in L (1)(Omega). We use a duality method, and, further, give estimates of first order derivatives for the resolvent and the semigroup, through properties of the generator in Sobolev spaces of negative order
Gradient estimates for perturbed Ornstein–Uhlenbeck semigroups on infinite-dimensional convex domains
No full textGeneration 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
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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