4 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…