Second-order boundary estimates for solutions to singular elliptic equations in borderline cases

Let \Omega \subsetR^N be a bounded smooth domain. We investigate the effect of the mean curvature of the boundary \partial \Omega on the behaviour of the solution to the homogeneous Dirichlet boundary value problem for the equation \Delta u + f(u) = 0. Under appropriate growth conditions on f(t) as t approaches zero, we find asymptotic expansions up to the second order of the solution in terms of the distance from x to the boundary \partial \Omega

Steiner symmetry in the minimization of the first eigenvalue in problems involving the p-Laplacian

Let Ω ⊂ ℝN be an open bounded connected set. We consider the eigenvalue problem −Δpu = λρ|u|p−2u in Ω with homogeneous Dirichlet boundary condition, where Δp is the p-Laplacian operator and ρ is an arbitrary function that takes only two given values 0 < α < β and that is subject to the constraint ∫Ω ρdx = αγ +β(|Ω|−γ) for a fixed 0 < γ < |Ω|. The optimization of the map ρ ↦ λ1(ρ), where λ1 is the first eigenvalue, has been studied by Cuccu, Emamizadeh and Porru. In this paper we consider a Steiner symmetric domain Ω and we show that the minimizers inherit the same symmetry

Problems for P-Monge-Ampere Equations

2010 Mathematics Subject Classification: 35A23, 35B51, 35J96, 35P30, 47J20, 52A40.We consider the homogeneous Dirichlet problem for a class of equations which generalize the p-Laplace equations as well as the Monge- Amp`ere equations in a strictly convex domain ⊂ Rn, n ≥ 2. In the sub-linear case, we study the comparison between quantities involving the solution to this boundary value problem and the corresponding quantities involving the (radial) solution of a problem in a ball having the same η1- mean radius as . Next, we consider the eigenvalue problem for such a p-Monge-Amp`ere equation and study a comparison between its principal eigenvalue (eigenfunction) and the principal eigenvalue (eigenfunction) of the corresponding problem in a ball having the same η1-mean radius as . Symmetrization techniques and comparison principles are the main tools used to get our results

Problems for p-Monge-Ampère equations

We consider the homogeneous Dirichlet problem for a class of equations which generalize the p-Laplace equations as well as the Monge- Amp`ere equations in a strictly convex domain Ω ⊂ Rn, n ≥ 2. In the sub-linear case, we study the comparison between quantities involving the solution to this boundary value problem and the corresponding quantities involving the (radial) solution of a problem in a ball having the same η1- mean radius as Ω. Next, we consider the eigenvalue problem for such a p-Monge-Amp`ere equation and study a comparison between its principal eigenvalue (eigenfunction) and the principal eigenvalue (eigenfunction) of the corresponding problem in a ball having the same η1-mean radius as Ω. Symmetrization techniques and comparison principles are the main tools used to get our results

Optical properties of Ge-oxygen defect center embedded in silica films

The photo-luminescence features of Ge-oxygen defect centers in a 100nm thick Ge-doped silica film on a pure silica substrate were investigated by looking at the emission spectra and time decay detected under synchrotron radiation excitation in the 10-300 K temperature range. This center exhibits two luminescence bands centered at 4.3eV and 3.2eV associated with its de-excitation from singlet (S1) and triplet (T1) states, respectively, that are linked by an intersystem crossing process. The comparison with results obtained from a bulk Ge-doped silica sample evidences that the efficiency of the intersystem crossing rate depends on the properties of the matrix embedding the Ge-oxygen defect centers, being more effective in the film than in the bulk counterpart.Comment: 10 pages, 3 figures, in press on J. Non cryst. solids (2007

Apparent digestibility of insect protein meals for rainbow trout

Insect meals are considered to be promising future ingredients for aquaculture feeds. In past feeding trials in rainbow trout, insect meals were included in diets only on the basis of their nutrients content and energy density without taking into account their biological availability due to the lack of their digestible values. Apparent digestibility (ADC) provides good indication of the bioavailability of nutrients and energy thus providing rational basis for the correct inclusion of feedstuffs. The aim of this research was to assess, in an in vivo trial on rainbow trout, the ADC of five full fat insect meals: one Tenebrio molitor (TM), two Hermetia illucens obtained through two different process (HI1 and HI2), one Musca domestica (MD), and one Alphitobius diaperinus (AD). Fish were fed a high-quality reference diet (R) and test diets obtained mixing the R diet with each of the test ingredients at a ratio of 70:30. Diets contained 1% celite as inert marker. Fish were fed to visual satiety twice a day and faecal samples collected using a continuous automatic device. Faeces were freeze dried and frozen (-20 \ub0C) until analyses. The ADC of dry matter, crude protein and ether extract of each insect meal diet were calculated. ADC for dry matter varied between 70.07 (HI1) and 80.85 (TM). ADC for protein was above 84% in all treatments and resulted the highest in MD, TM and AD treatments. Ether extract apparent digestibility significantly differed among diets with the highest value reported for TM treatment. All treatments reported values higher than 96%. Observed differences could be due to the insect species and meal treatment but in general, tested insect meals were highly digestible for rainbow trout. The results from this research could be useful to optimize the diet formulation

Renal function and physical fitness after 12-mo supervised training in kidney transplant recipients

To evaluate the effect of a 12-mo supervised aerobic and resistance training, on renal function and exercise capacity compared to usual care recommendations