Related papers: On the electrostatic Born-Infeld equation with ext…
In this paper, we consider the electrostatic Born-Infeld model \begin{equation*} \tag{$\mathcal{BI}$} \left\{ \begin{array}{rcll} -\operatorname{div}\left(\displaystyle\frac{\nabla \phi}{\sqrt{1-|\nabla \phi|^2}}\right)&=& \rho & \hbox{in…
We consider the electrostatic Born-Infeld energy \begin{equation*} \int_{\mathbb{R}^N}\left(1-{\sqrt{1-|\nabla u|^2}}\right)\, dx -\int_{\mathbb{R}^N}\rho u\, dx, \end{equation*} where $\rho \in L^{m}(\mathbb{R}^N)$ is an assigned charge…
In this paper, we study the static Born-Infeld equation $$ -\mathrm{div}\left(\frac{\nabla u}{\sqrt{1-|\nabla u|^2}}\right)=\sum_{k=1}^n a_k\delta_{x_k}\quad\mbox{in }\mathbb R^N,\qquad \lim_{|x|\to\infty}u(x)=0, $$ where $N\ge3$,…
In this note, we present a new proof of the solvability of the electrostatic Born-Infeld equation with radial charge, based on the conformal method and the Spacetime Positive Energy Theorem. An advantage of this approach is that the…
More than 80 years ago, Born-Infeld electrodynamics was proposed in order to remove the point charge singularity in Maxwell electrodynamics. In this work, after a brief introduction to Lagrangian formulation of Abelian Born-Infeld model in…
We study the minimizer of the electrostatic Born--Infeld energy \begin{equation*} \int_{\mathbb{R}^n}1-\sqrt{1-|D v|^2}\ dx-\int_{\mathbb{R}^n}\rho v\ dx, \end{equation*} which vanishes at infinity. We show that the minimizer $u$ is…
In this work we discuss the properties of a modified Born-Infeld electrodynamics in the framework of very special relativity (VSR). This proposal allows us to study VSR mass effects in a gauge-invariant context of nonlinear electrodynamics.…
The Born-Infeld equation in the plane is usefully captured in complex language. The general exact solution can be written as a combination of holomorphic and anti-holomorphic functions. However, this solution only expresses the potential in…
In this paper, using variational methods, we look for non-trivial solutions for the following problem $$ \begin{cases} -{\rm div}\left(a(|\nabla u|^2)\nabla u\right)=g(u), & \hbox{in }\mathbb{R}^N,\; N\geq 3, \\[1mm] u(x)\to 0, &\hbox{as…
Born-Infeld (BI) electrodynamics is motivated by the infinite self-energy of the point charge in Maxwell electrodynamics. In BI electrodynamics, an upper bound $b$ is imposed on the electric field, thus limiting the self-energy of the point…
We study the Einstein-Klein-Gordon system coupled to the Born-Infeld electrodynamics. We explore the solution space of a static spherically symmetric, complex scalar field minimally coupled to both gravitational and electromagnetic fields.…
Starting from the microscopic reduced Hartree-Fock equation, we derive the nanoscopic linearized Poisson-Boltzmann equation for the electrostatic potential associated with the electron density.
We propose a new model of nonlinear electrodynamics with three parameters. Born-Infeld electrodynamics and exponential electrodynamics are particular cases of this model. The phenomenon of vacuum birefringence is studied. We show that there…
Given a measure $\rho$ on a domain $\Omega \subset \mathbb{R}^m$, we study spacelike graphs over $\Omega$ in Minkowski space with Lorentzian mean curvature $\rho$ and Dirichlet boundary condition on $\partial \Omega$. The graph function…
We study the effect of the limiting field strength of Born-Infeld electromagnetism on the dynamics of charged particle scattering. We formulate the Born-Infeld limiting field in an invariant manner, showing that it is the electric…
We extensively explore three different aspects of Born-Infeld (BI) type nonlinear $U(1)$ gauge-invariant modifications of Maxwell's classical electrodynamics (also known as BI-type nonlinear electrodynamics) and bring some new perspectives…
The complex method to obtain 2-dimensional Born-Infeld electrostatic solutions is presented in a renewed form. The solutions are generated by a holomorphic seed that makes contact with the Coulombian complex potential. The procedure is…
We investigate $f(T)$ theory coupled with a nonlinear source of electrodynamics, for a spherically symmetric and static spacetime in $4D$. We re-obtain the Born-Infeld and Reissner-Nordstrom-AdS solutions. We generalize the no-go theorem…
Within the context of Born-Infeld (BI) nonlinear electrodynamics (NED) we revisit the non-relativistic, spinless H-atom. The pair potential computed from the Born-Infeld equations is approximated by the Morse type potential with remarkable…
We discuss the formation of scalar clouds on charged, spherically symmetric and static stars and black holes. We first discuss Reissner-Nordstr\"om black holes with electric and magnetic charge and present new results demonstrating the…