Related papers: Inequalities for the lowest magnetic Neumann eigen…
This paper concerns the shape optimization problem of minimizing the ground state energy of the magnetic Dirichlet Laplacian with constant magnetic field among three-dimensional domains of fixed volume. In contrast to the two-dimensional…
In this paper we study the eigenvalue sums of Dirichlet Laplacians on bounded domains. Among our results we establish an improvement of the Li-Yau bound in the presence of a constant magnetic field.
We consider a compact Riemannian manifold M endowed with a potential 1-form A and study the magnetic Laplacian associated with those data (with Neumann magnetic boundary condition if the bpoundary of M is not empty). We first establish a…
This paper studies the optimization of the lowest eigenvalue of the magnetic Steklov problem on planar domains. In the bounded domain setting and for magnetic fields of moderate strengths, we prove that among all simply-connected smooth…
In this paper we study optimization problems for Neumann eigenvalues $\mu_k$ among convex domains with a constraint on the diameter or the perimeter. We work mainly in the plane, though some results are stated in higher dimension. We study…
For the magnetic Laplacian on a bounded planar domain, imposing Neumann boundary conditions produces eigenvalues below the lowest Landau level. If the domain has two boundary components and one imposes a Neumann condition on one component…
Given a convex domain and its convex sub-domain we prove a variant of domain monotonicity for the Neumann eigenvalues of the Laplacian. As an application of our method we also obtain an upper bound for Neumann eigenvalues of the Laplacian…
We consider the Neumann realization of the magnetic laplacian in $\mathbb{R}^3_+$, in the case in which the magnetic field has a piecewise constant strength and a uniform direction. This operator is expected to be an effective model in…
Inspired by a paper by T. Chakradhar, K. Gittins, G. Habib and N. Peyerimhoff, we analyze their conjecture that the ground state energy of the magnetic Dirichlet-to-Neumann operator tends to infinity as the magnetic field tends to infinity.…
The core result of this paper is an upper bound for the ground state energyof the magnetic Laplacian with constant magnetic field on cones that are contained in ahalf-space. This bound involves a weighted norm of the magnetic field related…
This article deals with the spectral analysis of the semiclassical Neumann magnetic Laplacian on a smooth bounded domain in dimension three. When the magnetic field is constant and in the semiclassical limit, we establish a four-term…
We consider the magnetic Dirichlet Laplacian with constant magnetic field on domains of finite measure. First, in the case of a disk, we prove that the eigenvalue branches with respect to the field strength behave asymptotically linear with…
The eigenvalue problem for the Laplacian on bounded, planar, convex domains with mixed boundary conditions is considered, where a Dirichlet boundary condition is imposed on a part of the boundary and a Neumann boundary condition on its…
In this paper, we obtain optimal upper bounds for all the Neumann eigenvalues in two situations (that are closely related). First we consider a one-dimensional Sturm-Liouville eigenvalue problem where the density is a function $h(x)$ whose…
We study the eigenvalue problem for the Neumann-Laplace operator in conformal regular planar domains $\Omega\subset\mathbb{C}$. Conformal regular domains support the Poincar\'e inequality and this allows us to estimate the variation of the…
The asymptotic behavior of the first eigenvalues of magnetic Laplacian operators with large magnetic fields and Neumann realization in smooth three-dimensional domains is characterized by model problems inside the domain or on its boundary.…
In 1996 Erdoes showed that among planar domains of fixed area, the smallest principal eigenvalue of the Dirichlet Laplacian with a constant magnetic field is uniquely achieved on the disk. We establish a quantitative version of this…
We consider the Schr\"odinger operator with constant transverse magnetic field on a half-plane, endowed with Neumann boundary conditions. We study the low energy currents flowing along the boundary and we establish a Limiting Absorption…
We provide the estimates for the constant in the weighted Poincar\'e inequality for a special class of planar domains and weights. Based on this, we prove the lower bounds for the first non-zero eigenvalue $\mu_\rho$ of the Neumann…
The sum of the first $n \geq 1$ eigenvalues of the Laplacian is shown to be maximal among triangles for the equilateral triangle, maximal among parallelograms for the square, and maximal among ellipses for the disk, provided the ratio…