14 papers
Quantitative uniform resolvent estimates
Piero D'Ancona, Jérémy Faupin, David Krejcirik
We derive quantitative uniform resolvent estimates for Schrödinger operators on the half-line with inverse-square potentials, which provide a sharp behaviour in the limit of large…
A reverse Faber--Krahn inequality for the Robin Laplacian with negative boundary parameter: small coupling in all dimensions
Nunzia Gavitone, David Krejcirik, Gloria Paoli
We establish Bareket's conjecture from 1977 for convex domains in all dimensions in the regime of weak boundary coupling. In other words, we consider the Laplace operator, subject…
Sharp estimates for the Laplacian torsional rigidity with negative Robin boundary conditions
Nunzia Gavitone, David Krejcirik, Gloria Paoli
Motivated by pioneering works of Bandle and Wagner, given a bounded Lipschitz domain with , we consider the Robin-Laplacian torsional rigidity $τ_α(Ω)…
Virtual bound states of the Pauli operator with an Aharonov-Bohm potential
Marie Fialova, David Krejcirik
A maximal realisation of the two-dimensional Pauli operator, subject to Aharonov--Bohm magnetic field, is investigated. Contrary to the case of the Pauli operator with regular magn…
Critical quasilinear Schroedinger equations with electromagnetic fields
Laura Baldelli, Roberta Filippucci, David Krejcirik
The p-Laplace operator in the entire N-dimensional Euclidean space, subject to external electromagnetic potentials, is investigated. In the general case 1<p<N, the existence of at…
Abrupt changes in the spectra of the Laplacian with constant complex magnetic field
David Krejcirik, Tho Nguyen Duc, Nicolas Raymond
We analyze the spectrum of the Laplace operator, subject to homogeneous complex magnetic fields in the plane. For real magnetic fields, it is well-known that the spectrum consists…
The relativistic rotated harmonic oscillator
A. Balmaseda, D. Krejcirik, J. M. Pérez-Pardo
We introduce a relativistic version of the non-self-adjoint operator obtained by a dilation analytic transformation of the quantum harmonic oscillator. While the spectrum is real a…
The Laplacian with complex magnetic fields
David Krejcirik, Tho Nguyen Duc, Nicolas Raymond
We study the two-dimensional magnetic Laplacian when the magnetic field is allowed to be complex-valued. Under the assumption that the imaginary part of the magnetic potential is r…
A note on the failure of the Faber-Krahn inequality for the vector Laplacian
David Krejcirik, Pier Domenico Lamberti, Michele Zaccaron
We consider a natural eigenvalue problem for the vector Laplacian related to stationary Maxwell's equations in a cavity and we prove that an analog of the celebrated Faber-Krahn in…
Spectral analysis of Dirac operators for dislocated potentials with a purely imaginary jump
Lyonell Boulton, David Krejcirik, Tho Nguyen Duc
In this paper we present a complete spectral analysis of Dirac operators with non-Hermitian matrix potentials of the form where . For …
The virial theorem and the method of multipliers in spectral theory
Lucrezia Cossetti, David Krejcirik
We provide a link between the virial theorem in functional analysis and the method of multipliers in theory of partial differential equations. After giving a physical insight into…
Dirac operators on the half-line: stability of spectrum and non-relativistic limit
David Kramar, David Krejcirik
We consider Dirac operators on the half-line, subject to generalised infinite-mass boundary conditions. We derive sufficient conditions which guarantee the stability of the spectru…
Spectral determinant for the wave equation on an interval with Dirac damping
David Krejcirik, Jiri Lipovsky
A closed formula for the spectral determinant for the wave equation on a bounded interval, subject to Dirichlet boundary conditions and an -multiple of the Dirac -type dampin…
Curved nonlinear waveguides
Laura Baldelli, David Krejcirik
The Dirichlet p-Laplacian in tubes of arbitrary cross-section along infinite curves in Euclidean spaces of arbitrary dimension is investigated. First, it is shown that the gap betw…