Zobrazeno 1 - 10
of 189
pro vyhledávání: '"Benguria, Rafael"'
We consider four-component Dirac operators on domains in the plane. With suitable boundary conditions, these operators describe graphene quantum dots. The most general boundary conditions are defined by a matrix depending on four real parameters. For
Externí odkaz:
http://arxiv.org/abs/2211.07568
In this paper we obtain a Hadamard type formula for simple eigenvalues and an analog to the Rayleigh-Faber-Krahn inequality for a class of nonlocal eigenvalue problems. Such class of equations include among others, the classical nonlocal problems wit
Externí odkaz:
http://arxiv.org/abs/2208.14979
In this manuscript, using a technique introduced by P.~T.~Nam in 2012 and the {\it Coulomb Uncertainty Principle}, we prove new bounds on the excess charge for non relativistic atomic systems, independent of the particle statistics. These new bounds
Externí odkaz:
http://arxiv.org/abs/2207.08328
Autor:
Benguria, Rafael D., Tubino, Trinidad
We prove an analytic bound on the excess charge for the Hartree equation in the atomic case.
Externí odkaz:
http://arxiv.org/abs/2201.13421
We investigate spectral features of the Dirac operator with infinite mass boundary conditions in a smooth bounded domain of $\mathbb{R}^2$. Motivated by spectral geometric inequalities, we prove a non-linear variational formulation to characterize it
Externí odkaz:
http://arxiv.org/abs/2003.04061
Inspired by the seminal, ground-breaking work of Abrikosov in 1957, we developed a new approximation to the interaction between two widely separated superconducting vortices. In contrast with Abrikosov's, we take into account the finite size of the v
Externí odkaz:
http://arxiv.org/abs/1912.03419
In this paper we analyse the spectrum of nonlocal Dirichlet problems with non-singular kernels in bounded open sets. The novelty is the continuity of eigenvalues with respect to domain perturbation via Lebesgue measure. Also, under additional smooth
Externí odkaz:
http://arxiv.org/abs/1911.05803
Autor:
Benguria, Rafael D., Benguria, Soledad
We develop a new method for estimating the region of the spectral parameter of a generalized Brezis--Nirenberg problem for which there are no, non trivial, smooth solutions. This new method combines the standard Rellich--Pohozaev argument with a Hard
Externí odkaz:
http://arxiv.org/abs/1901.09958
In this paper we study the existence and non-existence of minimizers for a type of (critical) Poincar\'{e}-Sobolev inequalities. We show that minimizers do exist for smooth domains in $\mathbb{R}^d$, an also for some polyhedral domains. On the other
Externí odkaz:
http://arxiv.org/abs/1810.05698
Here we prove an isoperimetric inequality for the harmonic mean of the first $N-1$ non-trivial Neumann eigenvalues of the Laplace-Beltrami operator for domains contained in a hemisphere of $\mathbb{S}^N$.
Externí odkaz:
http://arxiv.org/abs/1809.05695