Caractérisation de quelques propriétés des problèmes aux limites pour les systèmes elliptiques : problèmes aux limites variationnel
Caractérisation de quelques propriétés des problèmes aux limites pour les systèmes elliptiques
Caractéristiques d'approximation des compacts dans les espaces fonctionnels et problèmes aux limites elliptiques
Coefficients des singularités pour des problèmes aux limites elliptiques sur un domaine à points coniques. I : Résultats généraux pour le problème de Dirichlet
Coefficients of singularities of the biharmonic problem of Neumann type: case of the crack.
Coefficients of the singularities on domains with conical points
As a model for elliptic boundary value problems, we consider the Dirichlet problem for an elliptic operator. Solutions have singular expansions near the conical points of the domain. We give formulas for the coefficients in these expansions.
Concentration phenomena for fourth-order elliptic equations with critical exponent.
Concentration phenomena for Liouville's equation in dimension four
Convergence of -cycle and -cycle multigrid methods for the biharmonic problem using the Morley element.
Convex shape optimization for the least biharmonic Steklov eigenvalue
The least Steklov eigenvalue d1 for the biharmonic operator in bounded domains gives a bound for the positivity preserving property for the hinged plate problem, appears as a norm of a suitable trace operator, and gives the optimal constant to estimate the L2-norm of harmonic functions. These applications suggest to address the problem of minimizing d1 in suitable classes of domains. We survey the existing results and conjectures about this topic; in particular, the existence of a convex domain...
Covariant differential operators and Green's functions
The basic idea of this paper is to use the covariance of a partial differential operator under a suitable group action to determine suitable associated Green’s functions. For instance, we offer a new proof of a formula for Green’s function of the mth power of the ordinary Laplace’s operator Δ in the unit disk found in a recent paper (Hayman-Korenblum, J. Anal. Math. 60 (1993), 113-133). We also study Green’s functions associated with mth powers of the Poincaré invariant Laplace operator . It turns...
Curved triangular finite -elements
Curved triangular -elements which can be pieced together with the generalized Bell’s -elements are constructed. They are applied to solving the Dirichlet problem of an elliptic equation of the order in a domain with a smooth boundary by the finite element method. The effect of numerical integration is studied, sufficient conditions for the existence and uniqueness of the approximate solution are presented and the rate of convergence is estimated. The rate of convergence is the same as in the...