The first eigenvalue of -Laplacian systems with nonlinear boundary conditions.
The generalized Morawetz problem for Lavrent'ev-Bitsadze equation with spectral parameter.
The Laplace-Beltrami operator in almost-Riemannian Geometry
We study the Laplace-Beltrami operator of generalized Riemannian structures on orientable surfaces for which a local orthonormal frame is given by a pair of vector fields that can become collinear.Under the assumption that the structure is 2-step Lie bracket generating, we prove that the Laplace-Beltrami operator is essentially self-adjoint and has discrete spectrum. As a consequence, a quantum particle cannot cross the singular set (i.e., the set where the vector fields become collinear) and the...
The linear symmetric systems associated with the modified Cherednik operators and applications
We introduce and study the linear symmetric systems associated with the modified Cherednik operators. We prove the well-posedness results for the Cauchy problem for these systems. Eventually we describe the finite propagation speed property of it.
The optimal shape of a dendrite sealed at both ends
The Schrödinger equation on non-stationary domains.
The second eigenvalue of the -Laplacian as goes to 1.
The simplified Wheeler-Dewitt equation : the Cauchy problem and some spectral properties
The sine-cosine method for the Davey-Stewartson equations.
The spectral cutting problem
The spectral properties of the Schrödinger operator in nonseparable Hilbert spaces
The Spectrum of the Continuous Laplacian on a Graph.
The squares of the Laplacian-Dirichlet eigenfunctions are generically linearly independent
The paper deals with the genericity of domain-dependent spectral properties of the Laplacian-Dirichlet operator. In particular we prove that, generically, the squares of the eigenfunctions form a free family. We also show that the spectrum is generically non-resonant. The results are obtained by applying global perturbations of the domains and exploiting analytic perturbation properties. The work is motivated by two applications: an existence result for the problem of maximizing the rate of...
The wave equation approach to an inverse problem for a general convex domain with impedance boundary conditions
Theorems of existence and multiplicity for nonlinear elliptic problems with noninvertible linear part
Théorie de la diffusion à courte portée pour des opérateurs à caractéristiques simples
Théorie de la diffusion pour l'équation de Schrödinger
Théorie de la diffusion pour les opérateurs analytiquement décomposables
Théorie des résonances pour des opérateurs de Schrödinger périodiques
Théorie spectrale de la propagation des ondes acoustiques dans un milieu stratifié perturbe