### Recent Submissions

• #### Quintessential inflation and cosmological seesaw mechanism: reheating and observational constraints ﻿

(2021-07)
Article
Restricted access - publisher's policy
Recently a new kind of quintessential inflation coming from the Lorentzian distribution has been introduced in [1,2]. The model leads to a very simple potential, which basically depends on two parameters, belonging to the ...

(Springer Nature, 2021-04-08)
Article
Restricted access - publisher's policy
We find upper bounds for the spherical cap discrepancy of the set of minimizers of the Riesz s-energy on the sphere Sd. Our results are based on bounds for a Sobolev discrepancy introduced by Thomas Wolff in an unpublished ...
• #### a-attractors in quintessential inflation motivated by supergravity ﻿

(American Physical Society, 2021-06-15)
Article
Open Access
An exponential kind of quintessential inflation potential motivated by supergravity is studied. This type belongs to the class of a-attractor models. The model was studied for the first time by Dimopoulos and Owen in [J. ...
• #### Theoretical and observational bounds on some interacting vacuum energy scenarios ﻿

(American Physical Society, 2021-04-15)
Article
Open Access
The dynamics of interacting dark matter-dark energy models is characterized through an interaction rate function quantifying the energy flow between these dark sectors. In most of the interaction functions, the expansion ...
• #### Near-sphere lattices with constant nonlocal mean curvature ﻿

(2018-04)
Article
Open Access
We are concerned with unbounded sets of RN whose boundary has constant nonlocal (or fractional) mean curvature, which we call CNMC sets. This is the equation associated to critical points of the fractional perimeter ...
• #### Discrepancies between observational data and theoretical forecast in single field slow roll inflation ﻿

(2016-09-09)
Article
Open Access
The PLANCK collaboration has determined, or greatly constrained, values for the spectral parameters of the CMB radiation, namely the spectral index ns, its running as, the running of the running ßs, using a growing body ...
• #### Optimal regularity of stable solutions to nonlinear equations involving the p-Laplacian ﻿

(2020-01-01)
Article
Open Access
We consider the equation-¿pu=f(u)in a smooth bounded domain ofRn, where¿pis thep-Laplaceoperator. Explicit examples of unbounded stable energy solutions are known ifn=p+4pp-1. Instead, whenn<p+4pp-1, stable solutions have ...
• #### Stability problems in nonautonomous linear differential equations in infinite dimensions ﻿

(2020-06-01)
Article
Open Access
In this paper we study the robustness of the stability in nonautonomous linear ordinary differential equations under integrally small perturbations in infinite dimensional Banach spaces. Some applications are obtained to ...
• #### Quintessential inflation for exponential type potentials: scaling and tracker behavior ﻿

(springer-Verlag, 2021-02)
Article
Open Access
We will show that for exponential type potentials of the form V(f)~e-¿fn/Mnpl, which are used to depict quintessential inflation, the solutions whose initial conditions take place during the slow roll phase in order to ...
• #### Calibrations and null-Lagrangians for nonlocal perimeters and an application to the viscosity theory ﻿

(2020-02-04)
Article
Restricted access - confidentiality agreement
For nonnegative even kernels K, we consider the K-nonlocal perimeter functional acting on sets. Assuming the existence of a foliation of space made of solutions of the associated K-nonlocal mean curvature equation in an ...
• #### Self-adjoint Dirac operators on domains in R-3 ﻿

(2020-06-20)
Article
Open Access
In this paper, the spectral and scattering properties of a family of self-adjoint Dirac operators in L2(O;C4), where O¿R3 is either a bounded or an unbounded domain with a compact C2-smooth boundary, are studied in a ...
• #### Stable solutions to semilinear elliptic equations are smooth up to dimension 9 ﻿

(2020-01-01)
Article
Open Access
In this paper we prove the following long-standing conjecture: stable solutions to semi-linear elliptic equations are bounded (and thus smooth) in dimension n¿9. This result, that was only known to be true for n¿4 , is ...