Circle-packing connections with random walks and a finite volume method
Cloaking via anomalous localized resonance for doubly complementary media in the quasistatic regime
This paper is devoted to the study of cloaking via anomalous localized resonance (CALR) in the two- and three-dimensional quasistatic regimes. CALR associated with negative index materials was discovered by Milton and Nicorovici [21] for constant plasmonic structures in the two-dimensional quasistatic regime. Two key features of this phenomenon are the localized resonance, i.e., the fields blow up in some regions and remain bounded in some others, and the connection between the localized resonance...
Codazzi tensors and equations of Monge-Ampère type on compact manifolds of constant sectional curvature.
Coefficients des singularités pour des problèmes aux limites elliptiques sur un domaine à points coniques. II : Quelques opérateurs particuliers
Coerciveness inequality for nonlocal boundary value problems for second order abstract elliptic differential equations.
Complete asymptotic expansions for eigenvalues of Dirichlet laplacian in thin three-dimensional rods
We consider the Dirichlet Laplacian in a thin curved three-dimensional rod. The rod is finite. Its cross-section is constant and small, and rotates along the reference curve in an arbitrary way. We find a two-parametric set of the eigenvalues of such operator and construct their complete asymptotic expansions. We show that this two-parametric set contains any prescribed number of the first eigenvalues of the considered operator. We obtain the complete asymptotic expansions for the eigenfunctions...
Complete asymptotic expansions for eigenvalues of Dirichlet Laplacian in thin three-dimensional rods*
We consider the Dirichlet Laplacian in a thin curved three-dimensional rod. The rod is finite. Its cross-section is constant and small, and rotates along the reference curve in an arbitrary way. We find a two-parametric set of the eigenvalues of such operator and construct their complete asymptotic expansions. We show that this two-parametric set contains any prescribed number of the first eigenvalues of the considered operator. We obtain the complete asymptotic expansions for the eigenfunctions...
Conditions aux limites approchées pour les couches minces périodiques
Conditions aux limites approchées pour les couches minces périodiques
Nous écrivons et nous justifions des conditions aux limites approchées pour des couches minces périodiques recouvrant un objet parfaitement conducteur en polarisation transverse électrique et transverse magnétique.
Conical diffraction by multilayer gratings: A recursive integral equation approach
The paper is devoted to an integral equation algorithm for studying the scattering of plane waves by multilayer diffraction gratings under oblique incidence. The scattering problem is described by a system of Helmholtz equations with piecewise constant coefficients in coupled by special transmission conditions at the interfaces between different layers. Boundary integral methods lead to a system of singular integral equations, containing at least two equations for each interface. To deal with...
Construction de laplaciens dont une partie finie (avec multiplicités) du spectre est donnée
Construction of compact constant mean curvature hypersurfaces with topology
In this paper, we explain how the end-to-end construction together with the moduli space theory can be used to produce compact constant mean curvature hypersurfaces with nontrivial topology. For the sake of simplicity, the hypersurfaces we construct have a large group of symmetry but the method can certainly be used to provide many more examples with less symmetries.
Continuous extendibility of solutions of the Neumann problem for the Laplace equation
A necessary and sufficient condition for the continuous extendibility of a solution of the Neumann problem for the Laplace equation is given.
Continuous extendibility of solutions of the third problem for the Laplace equation
A necessary and sufficient condition for the continuous extendibility of a solution of the third problem for the Laplace equation is given.
Contribution à la résolution numérique des équations de Laplace et de la chaleur
Convergence of a Finite Difference Method for the Third BVP for Poisson's Equation
Convergence of Cell Based Finite Volume Discretizations for Problems of Control in the Conduction Coefficients
We present a convergence analysis of a cell-based finite volume (FV) discretization scheme applied to a problem of control in the coefficients of a generalized Laplace equation modelling, for example, a steady state heat conduction. Such problems arise in applications dealing with geometric optimal design, in particular shape and topology optimization, and are most often solved numerically utilizing a finite element approach. Within the FV framework for control in the coefficients problems ...
Convergence of Cell Based Finite Volume Discretizations for Problems of Control in the Conduction Coefficients
We present a convergence analysis of a cell-based finite volume (FV) discretization scheme applied to a problem of control in the coefficients of a generalized Laplace equation modelling, for example, a steady state heat conduction. Such problems arise in applications dealing with geometric optimal design, in particular shape and topology optimization, and are most often solved numerically utilizing a finite element approach. Within the FV framework for control in the coefficients problems ...
Convergence of dual finite element approximations for unilateral boundary value problems
A semi-coercive problem with unilateral boundary conditions of the Signoriti type in a convex polygonal domain is solved on the basis of a dual variational approach. Whereas some strong regularity of the solution has been assumed in the previous author’s results on error estimates, no assumption of this kind is imposed here and still the -convergence is proved.
Convergence of Finite-difference Schemes for Poisson's Equation With Boundary Condition of the Third Kind