129 citations · 369 across the 23 of their papers we have counts for
24 papers
End-point non-regularity of the Dirichlet problem on Lipschitz domains -- An elementary proof
Martin Costabel, Monique Dauge
We construct a plane Lipschitz domain for which the range of the Laplace operator from to is not closed. We show that rapid oscillations of the bound…
Estimates for harmonic functions near pseudo-corners
Martin Costabel, Monique Dauge
It is well known that derivatives of solutions to elliptic boundary value problems may become unbounded near the corner of a domain with a conical singularity, even if the data are…
Dirichlet problem on perturbed conical domains via converging generalized power series
Martin Costabel, Matteo Dalla Riva, Monique Dauge +1
We consider the Poisson equation with homogeneous Dirichlet conditions in a family of domains in indexed by a small parameter . The domains depend on only within a b…
Convergence of a simple discretization of the finite Hilbert transformation
Martin Costabel
For a singular integral equation on an interval of the real line, we study the behavior of the error of a delta-delta discretization. We show that the convergence is non-uniform, b…
Stability Analysis of a Simple Discretization Method for a Class of Strongly Singular Integral Equations
Martin Costabel, Monique Dauge, Khadijeh Nedaiasl
Motivated by the discrete dipole approximation (DDA) for the scattering of electromagnetic waves by a dielectric obstacle that can be considered as a simple discretization of a Lip…
Characterization of Sobolev spaces by their Fourier coefficients in axisymmetric domains
Martin Costabel, Monique Dauge, Jun-Qi Hu
Using Fourier series representations of functions on axisymmetric domains, we find weighted Sobolev norms of the Fourier coefficients of a function that yield norms equivalent to t…
Maxwell eigenmodes in product domains
Martin Costabel, Monique Dauge
This paper is devoted to Maxwell modes in three-dimensional bounded electromagnetic cavities that have the form of a product of lower dimensional domains in some system of coordina…
On the limit Sobolev regularity for Dirichlet and Neumann problems on Lipschitz domains
Martin Costabel
We construct a bounded domain in for which the regularity for the Dirichlet and Neumann problems for the Laplacian cannot be improved, that is, there…
Converging expansions for Lipschitz self-similar perforations of a plane sector
Martin Costabel, Matteo Dalla Riva, Monique Dauge +1
In contrast with the well-known methods of matching asymptotics and multiscale (or compound) asymptotics, the " functional analytic approach " of Lanza de Cristoforis (Analysis 28,…
Continuity properties of the inf-sup constant for the divergence
Christine Bernardi, Martin Costabel, Monique Dauge +1
The inf-sup constant for the divergence, or LBB constant, is explicitly known for only few domains. For other domains, upper and lower estimates are known. If more precise values a…
Inequalities of Babuška-Aziz and Friedrichs-Velte for differential forms
Martin Costabel
For sufficiently smooth bounded plane domains, the equivalence between the inequalities of Babu{\v s}ka --Aziz for right inverses of the divergence and of Friedrichs on conjugate h…
Volume integral equations for electromagnetic scattering in two dimensions
Martin Costabel, Eric Darrigrand, Hamdi Sakly
We study the strongly singular volume integral equation that describes the scattering of time-harmonic electromagnetic waves by a penetrable obstacle. We consider the case of a cyl…
On the Spectrum of Volume Integral Operators in Acoustic Scattering
M. Costabel
Volume integral equations have been used as a theoretical tool in scattering theory for a long time. A classical application is an existence proof for the scattering problem based…
The inf-sup constant for the divergence on corner domains
Martin Costabel, Michel Crouzeix, Monique Dauge +1
The inf-sup constant for the divergence, or LBB constant, is related to the Cosserat spectrum. It has been known for a long time that on non-smooth domains the Cosserat operator ha…
On the inequalities of Babuška-Aziz, Friedrichs and Horgan-Payne
Martin Costabel, Monique Dauge
The equivalence between the inequalities of Babuška-Aziz and Friedrichs for sufficiently smooth bounded domains in the plane has been shown by Horgan and Payne 30 years ago. We pro…
Primal and Shadow functions, Dual and Dual-Shadow functions for a circular crack and a circular 90 degree V-notch with Neumann boundary conditions
Samuel Shannon, Zohar Yosibash, Monique Dauge +1
This report presents explicit analytical expressions for the primal, primal shadows, dual and dual shadows functions for the Laplace equation in the vicinity of a circular singular…
Shape derivatives of boundary integral operators in electromagnetic scattering. Part II : Application to scattering by a homogeneous dielectric obstacle
Martin Costabel, Frédérique Le Louër
We develop the shape derivative analysis of solutions to the problem of scattering of time-harmonic electromagnetic waves by a bounded penetrable obstacle. Since boundary integral…
Shape derivatives of boundary integral operators in electromagnetic scattering. Part I: Shape differentiability of pseudo-homogeneous boundary integral operators
Martin Costabel, Frédérique Le Louër
In this paper we study the shape differentiability properties of a class of boundary integral operators and of potentials with weakly singular pseudo-homogeneous kernels acting bet…
Potential maps, Hardy spaces, and tent spaces on special Lipschitz domains
Martin Costabel, Alan McIntosh, Robert J. Taggart
Suppose that is the open region in above a Lipschitz graph and let denote the exterior derivative on . We construct a convolution operator …
Shape derivatives of boundary integral operators in electromagnetic scattering
Martin Costabel, Frédérique Le Louër
We develop the shape derivative analysis of solutions to the problem of scattering of time-harmonic electromagnetic waves by a bounded penetrable obstacle. Since boundary integral…
Analytic Regularity for Linear Elliptic Systems in Polygons and Polyhedra
Martin Costabel, Monique Dauge, Serge Nicaise
We prove weighted anisotropic analytic estimates for solutions of second order elliptic boundary value problems in polyhedra. The weighted analytic classes which we use are the sam…
On the Kleinman-Martin integral equation method for electromagnetic scattering by a dielectric body
Martin Costabel, Frédérique Le Louër
The interface problem describing the scattering of time-harmonic electromagnetic waves by a dielectric body is often formulated as a pair of coupled boundary integral equations for…
Discrete compactness for the p-version of discrete differential forms
Daniele Boffi, Martin Costabel, Monique Dauge +2
In this paper we prove the discrete compactness property for a wide class of p-version finite element approximations of non-elliptic variational eigenvalue problems in two and thre…
On Bogovski\uı and regularized Poincaré integral operators for de Rham complexes on Lipschitz domains
Martin Costabel, Alan McIntosh
We study integral operators related to a regularized version of the classical Poincaré path integral and the adjoint class generalizing Bogovski\uı's integral operator, acting on d…