Elliptic and degenerate-elliptic operators in unbounded domains
Elliptic corner operators in spaces with continuous radial asymptotics II
Asymptotic expansions at the origin with respect to the radial variable are established for solutions to equations with smooth 2-dimensional singular Fuchsian type operators.
Embedded eigenvalues and resonances of Schrödinger operators with two channels
In this article, we give a necessary and sufficient condition in the perturbation regime on the existence of eigenvalues embedded between two thresholds. For an eigenvalue of the unperturbed operator embedded at a threshold, we prove that it can produce both discrete eigenvalues and resonances. The locations of the eigenvalues and resonances are given.
Équations d'évolution en norme uniforme (conditions nécessaires et suffisantes de résolution et holomorphie)
Equivalence of Boundary Eigenvalue Operator Fuctions and their Characteristic Matrix Functions.
Erratum to “Non-trapping condition for semiclassical Schrödinger operators with matrix-valued potentials”.
Essential self-adjointness for magnetic Schrödinger operators on non-compact manifolds
We give a condition of essential self-adjointness for magnetic Schrödinger operators on non-compact Riemannian manifolds with a given positive smooth measure which is fixed independently of the metric. This condition is related to the classical completeness of a related classical hamiltonian without magnetic field. The main result generalizes the result by I. Oleinik [29,30,31], a shorter and more transparent proof of which was provided by the author in [41]. The main idea, as in [41], consists...
Essential Selfadjointness of Dirac Operators with a Strongly Singular Potential.
Essential Self-Adjointness of Schrödinger Operators Bounded from Below.
Estimate of the Hausdorff measure of the singular set of a solution for a semi-linear elliptic equation associated with superconductivity
We study the boundedness of the Hausdorff measure of the singular set of any solution for a semi-linear elliptic equation in general dimensional Euclidean space . In our previous paper, we have clarified the structures of the nodal set and singular set of a solution for the semi-linear elliptic equation. In particular, we showed that the singular set is -rectifiable. In this paper, we shall show that under some additive smoothness assumptions, the -dimensional Hausdorff measure of singular set...
Estimates for a number of negative eigenvalues of the Schrödinger operator with intensive magnetic field
Estimates for the cut-off resolvent of the Laplacian for trapping obstacles
Estimation du reste dans la théorie spectrale d'une classe de problèmes d'opérateur elliptiques dégénérés
Étude semi-classique d'observables quantiques
Existence et prolongement des solutions holomorphes des équations aux dérivées partielles
Existence locale de solutions holomorphes pour les équations différentielles d'ordre infini
L’existence de solutions holomorphes locales d’équations aux dérivées partielles d’ordre infini à coefficients holomorphes de type spécial est étudiée.
Existence of multiple principal eigenvalues for some indefinite linear eigenvalue problems
We study the existence of principal eigenvalues for differential operators of second order which are not necessarily in divergence form. We obtain results concerning multiplicity of principal eigenvalues in both the variational and the general case. Our approach uses systematically the Krein-Rutman theorem and fixed point arguments for the spectral radius of some associated problems. We also use a variational characterization for both the self-adjoint and the general case.
Existence of solutions for transversally elliptic left invariant differential operators on nilpotent Lie groups
Existence theorems for operator equations and nonlinear elliptic boundary-value problems
Extension of zero-solutions of partial differential operators with dominating principal part.