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Optimal regularity of stable solutions to nonlinear equations involving the pLaplacian
(20200101)
Article
Restricted access  publisher's policyWe consider the equation¿pu=f(u)in a smooth bounded domain ofRn, where¿pis thepLaplaceoperator. Explicit examples of unbounded stable energy solutions are known ifn=p+4pp1. Instead, whenn<p+4pp1, stable solutions have ... 
Stability problems in nonautonomous linear differential equations in infinite dimensions
(20200601)
Article
Open AccessIn 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
(springerVerlag, 202102)
Article
Open AccessWe 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 nullLagrangians for nonlocal perimeters and an application to the viscosity theory
(20200204)
Article
Restricted access  confidentiality agreementFor nonnegative even kernels K, we consider the Knonlocal perimeter functional acting on sets. Assuming the existence of a foliation of space made of solutions of the associated Knonlocal mean curvature equation in an ... 
Selfadjoint Dirac operators on domains in R3
(20200620)
Article
Restricted access  publisher's policyIn this paper, the spectral and scattering properties of a family of selfadjoint Dirac operators in L2(O;C4), where O¿R3 is either a bounded or an unbounded domain with a compact C2smooth boundary, are studied in a ... 
Stable solutions to semilinear elliptic equations are smooth up to dimension 9
(20200101)
Article
Open AccessIn this paper we prove the following longstanding conjecture: stable solutions to semilinear elliptic equations are bounded (and thus smooth) in dimension n¿9. This result, that was only known to be true for n¿4 , is ... 
Matter Bounce Scenario in F(T) gravity
(2016)
Article
Open AccessIt is shown that teleparallel F(T) theories of gravity combined with holonomy corrected Loop Quantum Cosmology (LQC) support a Matter Bounce Scenario (MBS) which is a potential alternative to the inflationary paradigm. The ... 
Viability of the Matter Bounce Scenario
(Institute of Physics (IOP), 2015)
Article
Open AccessIt is shown that teleparallel F(T) theories of gravity combined with Loop Quantum Cosmology support a Matter Bounce Scenario which is an alternative to the inflation scenario in the Big Bang paradigm. It is checked that ... 
Note on the reheating temperature in Starobinskytype potentials
(Springer Nature, 202012)
Article
Open AccessThe relation between the reheating temperature, the number of efolds and the spectral index is shown for the Starobinsky model and some of its descendants through a very detailed calculation of these three quantities. The ... 
The spectrum of gravitational waves, their overproduction in quintessential inflation and its influence in the reheating temperature
(20200601)
Article
Open AccessOne of the most important issues in an inflationary theory as standard or quintessential inflation is the mechanism to reheat the universe after the end of the inflationary period in order to match with the Hot Big Bang ... 
Understanding the phenomenology of interacting dark energy scenarios and their theoretical bounds
(American Physical Society (APS), 20200615)
Article
Open AccessNongravitational interaction between dark matter and dark energy has been considered in a spatially flat FriedmannLemaîtreRobertsonWalker (FLRW) universe. The interaction rate is assumed to be linear in the energy ... 
Scaling solutions in quintessential inflation
(springerVerlag, 202005)
Article
Open AccessIn quintessence scalar field theories, the presence of scaling solutions are important during the radiation and matter epoch due to having their attractor character. Usually, it is assumed that the initial conditions of ...