# Benhellal BadreddineCarl von Ossietzky Universität Oldenburg

Benhellal Badreddine

## About

11

Publications

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49

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Introduction

## Publications

Publications (11)

In a recent paper Behrndt, Holzmann, and Stenzel introduced a new class of two-dimensional Schr\"odinger operators with oblique transmissions along smooth curves. We extend most components of this analysis to the case of Lipschitz curves.

We study the self-adjointness of the two-dimensional Dirac operator coupled with electrostatic and Lorentz scalar shell interactions of constant strength $\varepsilon$ and $\mu$ supported on a closed Lipschitz curve. Namely, we present several new explicit ranges of $\varepsilon$ and $\mu$ for which there is a unique self-adjoint realization with d...

We discuss the spectral properties of three-dimensional Dirac operators with critical combinations of electrostatic and Lorentz scalar shell interactions supported by a compact smooth surface. It turns out that the criticality of the interaction may result in a new interval of essential spectrum. The position and the length of the interval are expl...

The purpose of this paper is to introduce and study Poincar\'e-Steklov (PS) operators associated to the Dirac operator $D_m$ with the so-called MIT bag boundary condition. In a domain $\Omega\subset\mathbb{R}^3$, for a complex number $z$ and for $U_z$ a solution of $(D_m-z)U_z=0$, the associated PS operator maps the value of $\Gamma_- U_z$, the MIT...

Let \(\Omega \subset {{\mathbb {R}}}^3\) be an open set. We study the spectral properties of the free Dirac operator \( \mathcal {H} :=- i \alpha \cdot \nabla + m\beta \) coupled with the singular potential \(V_\kappa =(\epsilon I_4 +\mu \beta + \eta (\alpha \cdot N))\delta _{\partial \Omega }\), where \(\kappa =(\epsilon ,\mu ,\eta )\in {{\mathbb...

Given an open set Ω⊂R3, we deal with the spectral study of Dirac operators of the form Ha,τ = H + Aa,τδ∂Ω, where H is the free Dirac operator in R3 and Aa,τ is a bounded, invertible, and self-adjoint operator in L²(∂Ω)⁴, depending on parameters (a,τ)∈R×Rn, n ⩾ 1. We investigate the self-adjointness and the related spectral properties of Ha,τ, such...

Given an open set $\Omega\subset\mathbb{R}^3$. We deal with the spectral study of Dirac operators of the form $H_{a,\tau}=H+A_{a,\tau}\delta_{\partial\Omega}$, where $H$ is the free Dirac operator in $\mathbb{R}^3$, $A_{a,\tau}$ is a bounded invertible, self-adjoint operator in $\mathit{L}^{2}(\partial\Omega)^4$, depending on parameters $(a,\tau)\i...

Let $\Omega\subset\mathbb{R}^3$ be an open set, we study the spectral properties of the free Dirac operator $\mathcal{H}$ coupled with the singular potential $V_\kappa=(\epsilon I_4 +\mu\beta+\eta(\alpha\cdot N))\delta_{\partial\Omega}$. In the first instance, $\Omega$ can be either a $\mathcal{C}^2$-bounded domain or a locally deformed half-space....

In this paper, we study a singular perturbation of a problem used in dimension two to model graphene or in dimension three to describe the quark confinement phenomenon in hadrons. The operators we consider are of the form $H + M\beta V (x)$, where $H$ is the free Dirac operator, $\beta$ is a constant matrix, $V (x)$ is a real valued piecewise const...