Generalized Gaussian Estimates for Elliptic Operators with Unbounded Coefficients on Domains

We consider second-order elliptic operators A in divergence form with coefficients belonging to Lloc∞(Ω), when Ω ⊆ ℝd is a sufficiently smooth (unbounded) domain. We prove that the realization of A in L2(Ω), with Neumann-type boundary conditions, generates a contractive, strongly continuous and analytic semigroup (T(t)) which has a kernel k satisfying generalized Gaussian estimates, written in terms of a distance function induced by the diffusion matrix and the potential term. Examples of operators where such a distance function is equivalent to the Euclidean one are also provided

On vector-valued Schrödinger operators with unbounded diffusion in Lp spaces

We 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

Generation of semigroups associated to strongly coupled elliptic operators in Lp(Rd;Rm)

A 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

Experimental studies by combined NDT of capillary rise monitoring in masonry specimens

In the case of Cultural Heritage a destructive or partly destructive investigation approach is rightly hindered by high protection measures. Nevertheless, for preservation purposes it is fundamental to deepen the knowledge about the various types of historic structures and their health state of conservation as well as on evolution of material decay due to environmental factors. The role of non destructive techniques (NDT) for assessment purposes becomes fundamental in these cases but their use is still not sufficiently widespread nor the technique\u2019s limits or possibilities are completely explored. Radar and infrared thermography are nondestructive investigation techniques becoming more frequently employed in diagnostics. This paper describes an integrated experimental approach based on infrared thermography and radar for the assessment of masonry structures. At a laboratory scale, the focus was placed onto their evaluation capacity to detect construction details and the beginning of material changes/deterioration and evolution with particular regard to moisture and brine capillary transport

Emission properties of Sm3+/Bi3+-doped YPO4 phosphor

International audienceThe luminescence properties of YPO4 phosphors activated with 2% Sm3+ and variable concentrations of Bi3+ (from 0 to 5%) have been investigated. Steady state emission and decay time measurements clearly evidence an increment of the emission performance as the Bi3+ content increases up to 2.5%. Quantum yield measurements provide quantitative confirmation of the experimental observations. This behavior has been associated to the effect of the Bi3+ ions on the optical properties of the host lattice