In this work we consider the two-dimensional Dirac operator with general local singular
interactions supported on a closed curve. A systematic study of the interaction is performed …

We study the point spectrum of the linearization at a solitary wave solution ϕ ω (x) e− i ω t to
the nonlinear Dirac equation in R n, for all n≥ 1, with the nonlinear term given by f (ψ⁎ β ψ) …

In this work we construct self-adjoint extensions of the Dirac operator associated to
Hermitian matrix potentials with Coulomb decay and prove that the domain is maximal. The …

Local smoothing estimates for the massless Dirac–Coulomb equation in 2 and 3 dimensions -
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In this paper we consider Dirac operators in R^ n R n, n ≥ 2 n≥ 2, with a potential V. Under
mild decay and continuity assumptions on V and some spectral assumptions on the …

We investigate $ L^ 1\to L^\infty $ dispersive estimates for the three dimensional Dirac
equation with a potential. We also classify the structure of obstructions at the thresholds of …

By developing the method of multipliers, we establish sufficient conditions which guarantee
the total absence of eigenvalues of the Laplacian in the half‐space, subject to variable …

Dispersive estimates for the Dirac equation in an Aharonov–Bohm field - ScienceDirect Skip
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We quantify the subcriticality of the bilaplacian in dimensions greater than four by providing
explicit repulsivity/smallness conditions on complex additive perturbations under which the …

Several recent papers have focused their attention in proving the correct analogue to the
Lieb-Thirring inequalities for non self-adjoint operators and in finding bounds on the …