74 citations · 409 across the 32 of their papers we have counts for
32 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…
Numerical simulation of Lugiato-Lefever equation for Kerr combs generation in Fabry-Perot resonators
Mouhamad Al Sayed Ali, Stéphane Balac, Germain Bourcier +5
Lugiato-Lefever equation (LLE) is a nonlinear Schrödinger equation with damping, detuning and driving terms, introduced as a model for Kerr combs generation in ring-shape resonator…
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…
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…
Corner asymptotics of the magnetic potential in the eddy-current model
Monique Dauge, Patrick Dular, Laurent Krähenbühl +3
In this paper, we describe the magnetic potential in the vicinity of a corner of a conducting body embedded in a dielectric medium in a bidimensional setting. We make explicit the…
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…
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…
Asymptotics for 2D whispering gallery modes in optical micro-disks with radially varying index
Stéphane Balac, Monique Dauge, Zoïs Moitier
Whispering gallery modes [WGM] are resonant modes displaying special features: They concentrate along the boundary of the optical cavity at high polar frequencies and they are asso…
Asymptotic Lattices, Good Labellings, and the Rotation Number for Quantum Integrable Systems
Monique Dauge, Michael A. Hall, San Vu Ngoc
This article introduces the notion of good labellings for asymptotic lattices in order to study joint spectra of quantum integrable systems from the point of view of inverse spectr…
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 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…
Dirichlet spectrum of the Fichera layer
Monique Dauge, Yvon Lafranche, Thomas Ourmières-Bonafos
We investigate the spectrum of the three-dimensional Dirichlet Laplacian in a prototypal infinite polyhedral layer, that is formed by three perpendicular quarter-plane walls of con…
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,…
High frequency oscillations of first eigenmodes in axisymmetric shells as the thickness tends to zero
Marie Chaussade-Beaudouin, Monique Dauge, Erwan Faou +1
The lowest eigenmode of thin axisymmetric shells is investigated for two physical models (acoustics and elasticity) as the shell thickness (2) tends to zero. Using a novel asymp…
Free Vibrations of Axisymmetric Shells: Parabolic and Elliptic cases
Marie Chaussade-Beaudouin, Monique Dauge, Erwan Faou +1
Approximate eigenpairs (quasimodes) of axisymmetric thin elastic domains with laterally clamped boundary conditions (Lam{é} system) are determined by an asymptotic analysis as the…
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…
Magnetic Laplacian in sharp three dimensional cones
Virginie Bonnaillie-Noël, Monique Dauge, Nicolas Popoff +1
The core result of this paper is an upper bound for the ground state energyof the magnetic Laplacian with constant magnetic field on cones that are contained in ahalf-space. This b…
Spectral asymptotics of the Dirichlet Laplacian in a conical layer
Monique Dauge, Thomas Ourmières-Bonafos, Nicolas Raymond
The spectrum of the Dirichlet Laplacian on conical layers is analysed through two aspects: the infiniteness of the discrete eigenvalues and their expansions in the small aperture l…
Ground state energy of the magnetic Laplacian on corner domains
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 smooth three-dimensional domains is character…
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…
Regularity for Maxwell eigenproblems in photonic crystal fibre modelling
Monique Dauge, Richard A. Norton, Robert Scheichl
The convergence behaviour and the design of numerical methods for modelling the flow of light in photonic crystal fibres depend critically on an understanding of the regularity of…
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…