Browsing Analysis of Partial Differential Equations (APDE) by Author "Ourmières-Bonafos, T."
Now showing items 1-6 of 6
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Dirac Operators and Shell Interactions: A Survey
(2021-01-01)In this survey we gather recent results on Dirac operators coupled with δ-shell interactions. We start by discussing recent advances regarding the question of self-adjointness for these operators. Afterwards we switch to ... -
On the bound states of Schrödinger operators with $\delta$-interactions on conical surfaces
(2016-06-30)In dimension greater than or equal to three, we investigate the spectrum of a Schrödinger operator with a $\delta$-interaction supported on a cone whose cross section is the sphere of codimension two. After decomposing ... -
Spectral asymptotics for $\delta$-interactions on sharp cones
(2017)We investigate the spectrum of three-dimensional Schr\"odinger operators with $\delta$-interactions of constant strength supported on circular cones. As shown in earlier works, such operators have infinitely many eigenvalues ... -
Spectral asymptotics of the Dirichlet Laplacian in a conical layer
(2015-05-01)The spectrum of the Dirichlet Laplacian on conical layers is analysed through two aspects: the infiniteness of the discrete eigenvalues and their expansions in the small aperture limit. On the one hand, we prove that, for ... -
Spectral Transitions for Aharonov-Bohm Laplacians on Conical Layers
(2016-07-11)We consider the Laplace operator in a tubular neighbourhood of a conical surface of revolution, subject to an Aharonov-Bohm magnetic field supported on the axis of symmetry and Dirichlet boundary conditions on the boundary ... -
A strategy for self-adjointness of Dirac operators: Applications to the MIT bag model and delta-shell interactions
Ourmières-Bonafos, T.; Vega, L.
(2016-12-21)
We develop an approach to prove self-adjointness of Dirac operators with boundary or transmission conditions at a $C^2$-compact surface without boundary. To do so we are lead to study the layer potential induced by the ...