Stability of a numerical method for solving the 3 D inverse scattering problem with fixed energy data.
Stability results for Harnack inequalities
We develop new techniques for proving uniform elliptic and parabolic Harnack inequalities on weighted Riemannian manifolds. In particular, we prove the stability of the Harnack inequalities under certain non-uniform changes of the weight. We also prove necessary and sufficient conditions for the Harnack inequalities to hold on complete non-compact manifolds having non-negative Ricci curvature outside a compact set and a finite first Betti number or just having asymptotically...
Stationary solutions of two-dimensional heterogeneous energy models with multiple species
We investigate stationary energy models in heterostructures consisting of continuity equations for all involved species, of a Poisson equation for the electrostatic potential and of an energy balance equation. The resulting strongly coupled system of elliptic differential equations has to be supplemented by mixed boundary conditions. If the boundary data are compatible with thermodynamic equilibrium then there exists a unique steady state. We prove that in a suitable neighbourhood of such a thermodynamic...
Störungstheoretische Regularitätsuntersuchungen.
Su alcune questioni connesse con il problema di derivata obliqua regolare per le funzioni armoniche
— Vengono riconsiderati il problema di derivata obliqua regolare e quello misto di Dirichlet-derivata obliqua regolare per le funzioni armoniche in un dominio di e le questioni di completezza hilbertiana connesse già studiate in un precedente lavoro e viene data una nuova dimostrazione di un teorema di unicità.
Sublinear elliptic equations in Rn.
Superconvergence by Steklov averaging in the finite element method
The Steklov postprocessing operator for the linear finite element method is studied. Superconvergence of order 𝓞(h²) is proved for a class of second order differential equations with zero Dirichlet boundary conditions for arbitrary space dimensions. Relations to other postprocessing and averaging schemes are discussed.
Superconvergence results for linear triangular elements
Superlinear CG convergence for special right-hand sides.
Sur la décroissance d’énergie locale du problème extérieur avec plusieurs obstacles strictement convexes
Sur la régularité locale des solutions de l’équation
Sur la théorie du potentiel dans les domaines de John.
Using rather elementary and direct methods, we first recover and add on some results of Aikawa-Hirata-Lundh about the Martin boundary of a John domain. In particular we answer a question raised by these authors. Some applications are given and the case of more general second order elliptic operators is also investigated. In the last parts of the paper two potential theoretic results are shown in the framework of uniform domains or the framework of hyperbolic manifolds.
Sur Le Comportement Asymptotique D'Une Transformation De La Fonction Spectrale De L'Opérateur De Laplace
Sur une méthode itérative de résolution de problèmes aux limites elliptiques non linéaires
Soit un opérateur non nécessairement linéaire d’un Hilbert de l’équation , pour donné dans . Nous étudions la convergence du schéma itératif suivant: aou est fonction d’un opérateur auto-adjoint choisi de telle sorte que l’inversion de soit immédiate numériquement. Par exemple avec un entier et une constante convenablement choisis. Nous appliquons les résultats à un problème aux limites non linéaires avec résultats numériques.
Sur une question de H. Brezis, M. Marcus et A. C. Ponce
Surge motion on a floating cylinder in water of finite depth.
Symmetry analysis of the cylindrical Laplace equation.
Symmetry problems 2
Some symmetry problems are formulated and solved. New simple proofs are given for some symmetry problems studied earlier. One of the results is as follows: if a single-layer potential of a surface, homeomorphic to a sphere, with a constant charge density, is equal to c/|x| for all sufficiently large |x|, where c > 0 is a constant, then the surface is a sphere.
Symplectic torus actions with coisotropic principal orbits
In this paper we completely classify symplectic actions of a torus on a compact connected symplectic manifold when some, hence every, principal orbit is a coisotropic submanifold of . That is, we construct an explicit model, defined in terms of certain invariants, of the manifold, the torus action and the symplectic form. The invariants are invariants of the topology of the manifold, of the torus action, or of the symplectic form.In order to deal with symplectic actions which are not Hamiltonian,...
Teoria De Puntos Criticos De Funciones Localmente Lipschitzianas Y Sus Aplicaciones.