[hal-00860318, v1] Magnetic Neumann Laplacian on a sharp cone
نویسندگان
چکیده
This paper is devoted to the spectral analysis of the Laplacian with constant magnetic field on a cone of aperture α and Neumann boundary condition. We analyze the influence of the orientation of the magnetic field. In particular, for any orientation of the magnetic field, we prove the existence of discrete spectrum below the essential spectrum in the limit α → 0 and establish a full asymptotic expansion for the n-th eigenvalue and the n-th eigenfunction.
منابع مشابه
Magnetic Neumann Laplacian on a sharp cone
This paper is devoted to the spectral analysis of the Laplacian with constant magnetic field on a cone of aperture α and Neumann boundary condition. We analyze the influence of the orientation of the magnetic field. In particular, for any orientation of the magnetic field, we prove the existence of discrete spectrum below the essential spectrum in the limit α → 0 and establish a full asymptotic...
متن کاملMagnetic Laplacian in sharp three dimensional cones
The core result of this paper is an upper bound for the ground state energy of the magnetic Laplacian with constant magnetic field on cones that are contained in a half-space. This bound involves a weighted norm of the magnetic field related to moments on a plane section of the cone. When the cone is sharp, i.e. when its section is small, this upper bound tends to 0. A lower bound on the essent...
متن کاملPeak power in the 3D magnetic Schrödinger equation
This paper is devoted to the spectral analysis of the magnetic Neumann Laplacian on an infinite cone of aperture α. When the magnetic field is constant and parallel to the revolution axis and when the aperture goes to zero, we prove that the first n eigenvalues exist and admit asymptotic expansions in powers of α.
متن کاملNonexistence and existence results for a 2$n$th-order $p$-Laplacian discrete Neumann boundary value problem
This paper is concerned with a 2nth-order p-Laplacian difference equation. By using the critical point method, we establish various sets of sufficient conditions for the nonexistence and existence of solutions for Neumann boundary value problem and give some new results. Results obtained successfully generalize and complement the existing ones.
متن کاملStrong Diamagnetism for General Domains and Applications
We consider the Neumann Laplacian with constant magnetic field on a regular domain. Let B be the strength of the magnetic field, and let λ1(B) be the first eigenvalue of the magnetic Neumann Laplacian on the domain. It is proved that B 7→ λ1(B) is monotone increasing for large B. Combined with the results of [FoHe2], this implies that all the ‘third’ critical fields for strongly Type II superco...
متن کامل