Stability estimates for resolvents, eigenvalues and eigenfunctions of elliptic operators on variable domains

We consider general second order uniformly elliptic operators subject to homogeneous boundary conditions on open sets $\phi (\Omega)$ parametrized by Lipschitz homeomorphisms $\phi$ defined on a fixed reference domain $\Omega$. Given two open sets $\phi (\Omega)$, $\tilde \phi (\Omega)$ we estimate the variation of resolvents, eigenvalues and eigenfunctions via the Sobolev norm $\|\tilde \phi -\phi \|_{W^{1,p}(\Omega)}$ for finite values of $p$, under natural summability conditions on eigenfunctions and their gradients. We prove that such conditions are satisfied for a wide class of operators and open sets, including open sets with Lipschitz continuous boundaries. We apply these estimates to control the variation of the eigenvalues and eigenfunctions via the measure of the symmetric difference of the open sets. We also discuss an application to the stability of solutions to the Poisson problem.Comment: 34 pages. Minor changes in the introduction and the refercenes. Published in: Around the research of Vladimir Maz'ya II, pp23--60, Int. Math. Ser. (N.Y.), vol. 12, Springer, New York 201

The PRIAMO study: age- and sex-related relationship between prodromal constipation and disease phenotype in early Parkinson's disease.

OBJECTIVES: To explore the impact of sex and age on relationship between prodromal constipation and disease phenotype in Parkinson's disease at early stages. METHODS: A total of 385 Parkinson's disease patients from the PRIAMO study were classified according to the presence of prodromal constipation and followed for 24 months. Multivariable mixed-effect models were applied. All analyses were performed separately for sex (64.1% men) and median age (different by sex: 67 years-old in men and 68 years-old in women). RESULTS: As for sex, prodromal constipation was associated with greater odds of attention/memory complaints and apathy symptoms in women only. As for age, prodromal constipation was associated with lower cognitive and higher apathy scores in older patients only. CONCLUSIONS: Prodromal constipation anticipates lower cognitive performances and more severe apathy since the earliest stages in women and older patients. Sex- and age-related heterogeneity of prodromal markers of Parkinson's disease may impact disease phenotype

The GLAST LAT tracker construction and test

GLAST is a next generation high-energy gamma-ray observatory designed for making observations of celestial gamma-ray sources in the energy band extending from 10 KeV to more than 300 GeV. Respect to the previous instrument EGRET, GLAST will have a higher effective area (six times more), higher field of view, energy range and resolution, providing an unprecedented advance in sensitivity (a factor 30 or more). The main scientific goals are the study of all gamma-ray sources such as blazars, gamma-ray bursts, supernova remnants, pulsars, diffuse radiation, and unidentified high-energy sources. The construction and test of the Large Area Telescope (LAT) tracker, has been a great effort during the past years, involving tens of people from many Italian INFN sections and industrial partners. Environmental and performance tests of the hardware, detectors and reading electronics, have been carried on during all the steps of the LAT construction. The resulting LAT performance are better than the ones required by the original science proposal, demonstrating the quality of the italian group effort. In this article we summarize the LAT construction and test workflow, presenting its main results

The GLAST LAT tracker construction and test

GLAST is a next generation high-energy gamma-ray observatory designed for making observations of celestial gamma-ray sources in the energy band extending from 10 KeV to more than 300 GeV. Respect to the previous instrument EGRET, GLAST will have a higher effective area (six times more), higher field of view, energy range and resolution, providing an unprecedented advance in sensitivity (a factor 30 or more). The main scientific goals are the study of all gamma-ray sources such as blazars, gamma-ray bursts, supernova remnants, pulsars, diffuse radiation, and unidentified high-energy sources. The construction and test of the Large Area Telescope (LAT) tracker, has been a great effort during the past years, involving tens of people from many Italian INFN sections and industrial partners. Environmental and performance tests of the hardware, detectors and reading electronics, have been carried on during all the steps of the LAT construction. The resulting LAT performance are better than the ones required by the original science proposal, demonstrating the quality of the italian group effort. In this article we summarize the LAT construction and test workflow, presenting its main results