On the heat trace of the magnetic Schrödinger operators on the hyperbolic plane.
On the linearization of some singular, nonlinear elliptic problems and applications
On the remainder in the Weyl formula for the Euclidean disk
We prove a 2-terms Weyl formula for the counting function of the spectrum of the Laplace operator in the Euclidean disk with a sharp remainder estimate .
On the solvability of semilinear elliptic equation via an associated eigenvaule problem.
On the Spectra of Schrödinger Operators with a Complex Potential.
On the spectral theory of pseudo-differential elliptic boundary problems
On the spectrum of a nonlinear planar problem
On the spectrum of the negative Laplacian for general doubly-connected bounded domains.
On the Wave Equation on a Compact Riemannian Manifold withour Conjugate Points.
Optimal energy decay rate of coupled wave equations.
Optimal observability of the multi-dimensional wave and Schrödinger equations in quantum ergodic domains
We consider the wave and Schrödinger equations on a bounded open connected subset of a Riemannian manifold, with Dirichlet, Neumann or Robin boundary conditions whenever its boundary is nonempty. We observe the restriction of the solutions to a measurable subset of during a time interval with . It is well known that, if the pair satisfies the Geometric Control Condition ( being an open set), then an observability inequality holds guaranteeing that the total energy of solutions can be...
Oscillateur quartique et méthodes semi-classiques