Asymptotically hyperbolic manifolds with polyhomogeneous metric

We analyze the resolvent and define the scattering matrix for asymptotically hyperbolic manifolds with metrics which have a polyhomogeneous expansion near the boundary, and also prove that there is always an essential singularity of the resolvent in this setting. We use this analysis to prove an inverse result for conformally compact odd dimensional Einstein manifolds.Comment: 22 pages, mistake on previous version correcte

On the viscosity solutions to some nonlinear elliptic equations

We consider viscosity solutions of a class of nonlinear degenerate elliptic equations on bounded domains. We prove comparison principles and a priori supremum bounds for the solutions. We also address the eigenvalue problem and, in many instances, show the existence of a first eigenvalue and a first positive eigenfunction.Comment: 33 pages. The work underwent a significant revision. The work has been expanded and generalized, relevant examples included and important references adde

A Phragm\'en-Lindel\"of property of viscosity solutions to a class of nonlinear, possibly degenerate, parabolic equations

We study Phragm\'en-Lindel\"of properties of viscosity solutions to a class of doubly nonlinear parabolic equations in $\mathbb{R}^n\times (0,T)$. We also include an application to some doubly nonlinear equations.Comment: 32 pages, small corrections are made, some needed conditions are adde

On the viscosity solutions to a degenerate parabolic differential equation

In this work, we study some properties of the viscosity solutions to a degenerate parabolic equation involving the non-homogeneous infinity-Laplacian.Comment: 45 pages 2 figure

An Eigenvalue problem for the Infinity-Laplacian

We study an eigenvalue problem for the infinity-Laplacian on bounded domains. We prove the existence of the principal eigenvalue and a corresponding positive eigenfunction. The work also contains existence results when the parameter, in the equation, is less than the first eigenvalue. A comparison principle applicable to these problems is also proven. Some additional results are shown, in particular, that on star- shaped domains and on C^2 domains higher eigenfunctions change sign. When the domain is a ball, we prove that the first eigenfunction has one sign, radial principal eigenfunction exist and are unique up to scalar multiplication, and that there are infinitely many eigenvalues.Comment: 36 pages Accepted to EJDE. Changes have been made to improve the expositio

On the viscosity solutions to Trudinger's equation

We study the existence of positive viscosity solutions to Trudinger's equation for cylindrical domains $\Omega\times[0, T)$, where $\Omega\subset \mathbb{R}^n,\;n\ge 2,$ is a bounded domain, $T>0$ and $2\leq p<\infty$. We show existence for general domains $\Omega,$ when $n<p<\infty$. For $2\leq p\leq n$, we prove existence for domains $\Omega$ that satisfy a uniform outer ball condition. We achieve this by constructing suitable sub-solutions and super-solutions and applying Perron's method.Comment: 25 pages, 2 figure

A Phragm\'en-Lindel\"of property of viscosity solutions to a class of doubly nonlinear parabolic equations: Bounded Case

We study Phragm\'en-Lindel\"of properties for viscosity solutions to a class of nonlinear parabolic equations of the type $H(Du, D^2u+Z(u)Du\otimes Du)+\chi(t)|Du|^\sigma-u_t=0$ under a certain boundedness condition on $H$. We also state results for positive solutions to a class of doubly nonlinear equation $H(Du, D^2u)-f(u)u_t=0$.Comment: 33 page

Asymptotics of viscosity solutions to some doubly nonlinear parabolic equations

We study asymptotic decay rates of viscosity solutions to some doubly nonlinear parabolic equations, including Trudinger's equation. We also prove a Phragm\'en-Lindel\"of type result and show its optimality.Comment: 26 pages. Some small changes and addition of optimality of the Phragm\'en-Lindel\"of type resul

Quel est l'impact de l'abolition des enseignants spécialistes au profit des enseignants généralistes sur la qualité de l'enseignement musical dans les niveaux 7-8 Harmos ?

Suite à la votation du 4 septembre 2011, la nouvelle loi sur l’enseignement obligatoire est entrée en vigueur. Une des conséquences les plus importantes de cette nouvelle loi a été la primarisation des niveaux 5 et 6 selon l’ancien système. De cela a découlé l’attribution de l’ensemble des branches de l’enseignement vaudois à des enseignants généralistes. Nous faisons l’hypothèse qu’un des avantages de cette décision est la mise en avant des compétences pédagogiques dans la transmission des savoirs. Le bon sens nous mène à croire que les branches utilisées quotidiennement comme le français, les mathématiques et les langues étrangères peuvent être enseignées grâce à une bonne préparation pédagogique des enseignants. Certaines branches, par contre, nécessitent des aptitudes et des connaissances particulières. Nous entendons par ceci, les disciplines comme les travaux manuels (aptitudes psychomotrices et créatives), l’éducation physique (aptitudes psychomotrices, physiques et sociales), les arts visuels (aptitudes psychomotrices et créatives) et la musique (aptitudes psychomotrices, affectives et créatives). Nous faisons l’hypothèse que les branches créatives ne peuvent pas être enseignées par tout un chacun, car elles nécessitent un entraînement spécifique qui ne fait pas forcément partie des activités quotidiennes de l’enseignant primair

Robust estimators for generalized linear models with a dispersion parameter

Highly robust and efficient estimators for the generalized linear model with a dispersion parameter are proposed. The estimators are based on three steps. In the first step the maximum rank correlation estimator is used to consistently estimate the slopes up to a scale factor. In the second step, the scale factor, the intercept, and the dispersion parameter are consistently estimated using a MT-estimator of a simple regression model. The combined estimator is highly robust but inefficient. Then, randomized quantile residuals based on the initial estimators are used to detect outliers to be rejected and to define a set S of observations to be retained. Finally, a conditional maximum likelihood (CML) estimator given the observations in S is computed. We show that, under the model, S tends to the complete sample for increasing sample size. Therefore, the CML tends to the unconditional maximum likelihood estimator. It is therefore highly efficient, while maintaining the high degree of robustness of the initial estimator. The case of the negative binomial regression model is studied in detail