Related papers: A Magnetic Contribution to the Hardy Inequality
A simple model of eddy currents in which current is computed solely from magnetic forces acting on electrons proves accessible to introductory students and gives a good qualitative account of eddy current forces. However, this model cannot…
We establish Trudinger-type inequality in the context of fractional boundary Hardy-type inequality for the case $sp=d$, where $p>1, ~ s \in (0,1)$ on a bounded Lipschitz domain $\Omega \subset \mathbb{R}^d$. In particular, we establish…
Hardy's uncertainty principle is a classical result in harmonic analysis, stating that a function in $L^2(\mathbb{R}^d)$ and its Fourier transform cannot both decay arbitrarily fast at infinity. In this paper, we extend this principle to…
The present work is concerned with existence of positive solutions for a class of fractional equation involving a Kirchhoff term and singular potential.
We study Schroedinger operators with periodic magnetic field in Euclidean 2-space, in the case of irrational magnetic flux. Positive measure Cantor spectrum is generically expected in the presence of an electric potential. We show that,…
One of the advantages of the finite energy sum rules is the fact that every operator in the operator product expansion series can be selected individually by the use of an appropriate kernel function which removes other operator poles. This…
We give an overview of the magnetic catalysis phenomenon. In the framework of quantum field theory, magnetic catalysis is broadly defined as an enhancement of dynamical symmetry breaking by an external magnetic field. We start from a brief…
In this article, we consider the 3D-rotating magnetohydrodynamic (MHD) system when the initial velocity and magnetic field both feature some 2D-part (i.-e. depending only on the horizontal space variables). We prove for weak and strong…
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…
We exhibit existence of non-trivial solutions of some fractional linear Schr\"odinger equations which are radial and vanish at the origin. This is in stark contrast to what happens in the local case. We also prove analogous results in the…
Due to any toroidal current column, the magnetic field is found to be sensitive as well as insensitive to its cross-sectional area depending on location of subject point, as predicted by numerical approaches [S. Aich, J. Thakkar, and J.…
In electrostatics, we can use either potential energy or field energy to ensure conservation of energy. In electrodynamics, the former option is unavailable. To ensure conservation of energy, we must attribute energy to the electromagnetic…
Using methods of weight functions, techniques of real analysis as well as the Hermite-Hadamard inequality, a half-discrete Hardy-Hilbert-type inequality with multi-parameters and a best possible constant factor related to the Hurwitz zeta…
The radial momentum operator in quantum mechanics is usually obtained through canonical quantization of the (symmetrical form of the) classical radial momentum. We show that the well known connection between the Hamiltonian of a free…
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…
In this paper, we study the asymptotic behavior of radial extremal functions to an inequality involving Hardy potential and critical Sobolev exponent. Based on the asymptotic behavior at the origin and the infinity, we shall deduce a strict…
We consider in this paper elliptic equations which are perturbations of Laplace's equation by a compactly supported potential. We show that in dimension greater than three for a wide class of potentials all the solutions are globally…
We revisit the Rellich inequality from the viewpoint of isolating the contributions from radial and spherical derivatives. This naturally leads to a comparison of the norms of the radial Laplacian and Laplace{Beltrami operators with the…
In this paper, we describe the magnetic potential in the vicinity of a corner of a conducting body embedded in a dielectric medium in a bidimensional setting. We make explicit the corner asymptotic expansion for this potential as the…
A critical look is taken at the calculation of the Casimir effect. The boundary conditions play an important role and should be imposed in a physical way. An acceptable result for the vacuum energy is only obtained when different…