1,720,993 research outputs found
Parabolic transmission eigenvalue-free regions in the degenerate isotropic case
No full textInternational audienceWe study the location of the transmission eigenvalues in the isotropic case when the restrictions of the refraction indices on the boundary coincide. Under some natural conditions we show that there exist parabolic transmission eigenvalue-free regions
SEMICLASSICAL PARAMETRIX FOR THE MAXWELL EQUATION AND APPLICATIONS TO THE ELECTROMAGNETIC TRANSMISSION EIGENVALUES
No full textInternational audienceWe introduce an analog of the Dirichlet-to-Neumann map for the Maxwell equation in a bounded domain. We show that it can be approximated by a pseudodifferential operator on the boundary with a matrix-valued symbol and we compute the principal symbol. As a consequence, we obtain a parabolic region free of the transmission eigenvalues associated to the Maxwell equation
APPROXIMATION OF THE ELASTIC DIRICHLET-TO-NEUMANN MAP
No full textInternational audienceWe study the Dirichlet-to-Neumann map for the stationary linear equation of elasticity in a bounded domain in R d , d ≥ 2, with smooth boundary. We show that it can be approximated by a pseudodifferential operator on the boundary with a matrix-valued symbol and we compute the principal symbol modulo conjugation by unitary matrices
IMPROVED RESOLVENT BOUNDS FOR RADIAL POTENTIALS
No full textInternational audienceWe prove semiclassical resolvent estimates for the Schrödinger operator in R d , d ≥ 3, with real-valued radial potentials V ∈ L ∞ (R d). In particular, we show that if V (x) = O x −δ with δ > 2, then the resolvent bound is of the form e Ch −4/3 with some constant C > 0. We also get resolvent bounds when 1 < δ ≤ 2. For slowly decaying α-Hölder potentials we get better resolvent bounds of the form e Ch −4/(α+3)
ASYMPTOTIC BEHAVIOR OF THE TRANSMISSION EIGENVALUES (Spectral and Scattering Theory and Related Topics)
Get PDFSEMI-CLASSICAL RESOLVENT ESTIMATES FOR L ∞ POTENTIALS ON RIEMANNIAN MANIFOLDS
No full textInternational audienceWe prove semi-classical resolvent estimates for the Schrödinger operator with a real-valued L ∞ potential on non-compact, connected Riemannian manifolds which may have a compact smooth boundary. We show that the resolvent bound depends on the structure of the man-ifold at infinity. In particular, we show that for compactly supported real-valued L ∞ potentials and asymptoticaly Euclidean manifolds the resolvent bound is of the form exp(Ch −4/3 log(h −1)), while for asymptoticaly hyperbolic manifolds it is of the form exp(Ch −4/3), where C > 0 is some constant
Sharp polynomial bounds on the number of scattering poles for metric perturbations of the Laplacian in IRn.
No full textPolynomial bounds on the number of scattering poles for metric perturbations of the Laplacian in {bf R}sp n, n≥3, odd
No full textSEMI-CLASSICAL RESOLVENT ESTIMATES FOR SHORT-RANGE L ∞ POTENTIALS
No full textInternational audienceWe prove semi-classical resolvent estimates for real-valued potentials V ∈ L ∞ (R n), n ≥ 3, satisfying V (x) = O x −δ with δ > 3
- …
