74 citations · 409 across the 32 of their papers we have counts for
10 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 influence of the geometry on skin effect in electromagnetism
Gabriel Caloz, Monique Dauge, Erwan Faou +1
We consider the equations of electromagnetism set on a domain made of a dielectric and a conductor subdomain in a regime where the conductivity is large. Assuming smoothness for th…
Trace Hardy inequality for the Euclidean space with a cut and its applications
Monique Dauge, Michal Jex, Vladimir Lotoreichik
We obtain a trace Hardy inequality for the Euclidean space with a bounded cut , . In this novel geometric setting, the Hardy-type inequality non-typic…
On the semiclassical Laplacian with magnetic field having self-intersecting zero set
Monique Dauge, Jean-Philippe Miqueu, Nicolas Raymond
This paper is devoted to the spectral analysis of the Neumann realization of the 2D magnetic Laplacian with semiclassical parameter h > 0 in the case when the magnetic field vanish…
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,…
Ground Energy of the Magnetic Laplacian in Polyhedral Bodies
Virginie Bonnaillie-Noël, Monique Dauge, Nicolas Popoff
The asymptotic behavior of the first eigenvalues of magnetic Laplacian operators with large magnetic fields and Neumann realization in polyhedral domains is characterized by a hier…
Plane waveguides with corners in the small angle limit
Monique Dauge, Nicolas Raymond
The plane waveguides with corners considered here are infinite V-shaped strips with constant thickness. They are parametrized by their sole opening angle. We study the eigenpairs o…
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…