129 citations · 369 across the 23 of their papers we have counts for
11 papers · 1 filter
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…
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,…
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…
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 …
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 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…