estimates for damped wave equations with odd initial data.
-perturbations of leading coefficients of elliptic operators: Asymptotics of eigenvalues.
L... Stability of Finite Element Approximations to Elliptic Gradient Equations.
L1 and L∞-estimates with a local weight for the ∂-equation on convex domains in Cn.
We construct a defining function for a convex domain in Cn that we use to prove that the solution-operator of Henkin-Romanov for the ∂-equation is bounded in L1 and L∞-norms with a weight that reflects not only how near the point is to the boundary of the domain but also how convex the domain is near the point. We refine and localize the weights that Polking uses in [Po] for the same type of domains because they depend only on the Euclidean distance to the boudary and don't take into account the...
L₁-uniqueness of degenerate elliptic operators
Let Ω be an open subset of with 0 ∈ Ω. Furthermore, let be a second-order partial differential operator with domain where the coefficients are real, and the coefficient matrix satisfies bounds 0 < C(x) ≤ c(|x|)I for all x ∈ Ω. If for some λ > 0 where then we establish that is L₁-unique, i.e. it has a unique L₁-extension which generates a continuous semigroup, if and only if it is Markov unique, i.e. it has a unique L₂-extension which generates a submarkovian semigroup. Moreover...
L2 Decay for the Navier-Stokes Flow in Halfspaces.
L2 estimates and existence theorems for the tangential Cauchy-Riemann complex.
L2 Estimates for the Finite Element Method for the Dirichlet Problem with Singular Data.
L2 stability analysis of the central discontinuous Galerkin method and a comparison between the central and regular discontinuous Galerkin methods
We prove stability and derive error estimates for the recently introduced central discontinuous Galerkin method, in the context of linear hyperbolic equations with possibly discontinuous solutions. A comparison between the central discontinuous Galerkin method and the regular discontinuous Galerkin method in this context is also made. Numerical experiments are provided to validate the quantitative conclusions from the analysis.
L²-data Dirichlet problem for weighted form Laplacians
We solve the L²-data Dirichlet boundary problem for a weighted form Laplacian in the unit Euclidean ball. The solution is given explicitly as a sum of four series.
L2-Integrability of Second Order Derivatives for Poisson's Equation in Nonsmooth Domains.
L2-stability of the upwind first order finite volume scheme for the Maxwell equations in two and three dimensions on arbitrary unstructured meshes
We investigate sufficient and possibly necessary conditions for the L2 stability of the upwind first order finite volume scheme for Maxwell equations, with metallic and absorbing boundary conditions. We yield a very general sufficient condition, valid for any finite volume partition in two and three space dimensions. We show this condition is necessary for a class of regular meshes in two space dimensions. However, numerical tests show it is not necessary in three space dimensions even on regular...
La condition de Hörmander-Kohn pour les opérateurs pseudo-différentiels
La condition nulle pour les équations hyperboliques en dimension deux d’espace
La conjecture de Kato
La diffraction en métrique de Schwarzschild : complétude asymptotique et résonances
La diffusione del calore in uno strato di spessore variabile in presenza di scambi termici non lineari con l'ambiente. (I) Deduzione di limitazioni a priori sulla temperatura e le sue derivate
La distribution des pôles de la matrice de diffusion
La finitude du nombre des lacunes de l'opérateur de Schrödinger bidimensionnel
La géométrie de Bakry-Émery et l’écart fondamental
Cet article est une présentation rapide, d’une part de résultats de l’auteur et Z. Lu [14], et d’autre part, de la résolution de la conjecture de l’écart fondamental par Andrews et Clutterbuck [1]. Nous commençons par rappeler ce qu’est la géométrie de Bakry-Émery, nous poursuivons en montrant les liens entre valeurs propres du laplacien de Dirichlet et de Neumann. Nous démontrons ensuite un rapport entre l’écart fondamental et la géométrie de Bakry-Émery, puis nous présentons les idées principales...