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  • Optimal regularity of stable solutions to nonlinear equations involving the p-Laplacian 

    Cabré Vilagut, Xavier; Miraglio, Pietro; Sanchón Rodellar, Manuel (2020-01-01)
    Article
    Restricted access - publisher's policy
    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 

    Munhoz Rodrigues, Hildebrando; Solà-Morales Rubió, Joan de; Nakassima, G. K. (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 

    Aresté Saló, Llibert; Haro Cases, Jaume (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 

    Cabré Vilagut, Xavier (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 

    Holzmann, Markus; Mas Blesa, Albert (2020-06-20)
    Article
    Restricted access - publisher's policy
    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 

    Cabré Vilagut, Xavier; Figalli, Alessio; Ros Oton, Xavier; Serra, Joaquim (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 ...

  • Matter Bounce Scenario in F(T) gravity 

    Haro Cases, Jaume; Amorós Torrent, Jaume (2016)
    Article
    Open Access
    It 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 

    Haro Cases, Jaume; Amorós Torrent, Jaume (Institute of Physics (IOP), 2015)
    Article
    Open Access
    It 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 Starobinsky-type potentials 

    Haro Cases, Jaume; Aresté Saló, Llibert (Springer Nature, 2020-12)
    Article
    Open Access
    The relation between the reheating temperature, the number of e-folds 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 

    Haro Cases, Jaume; Aresté Saló, Llibert (2020-06-01)
    Article
    Open Access
    One 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 

    Pan, Supriya; Haro Cases, Jaume; Yang, Weiqiang; Amorós Torrent, Jaume (American Physical Society (APS), 2020-06-15)
    Article
    Open Access
    Nongravitational interaction between dark matter and dark energy has been considered in a spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) universe. The interaction rate is assumed to be linear in the energy ...

  • Scaling solutions in quintessential inflation 

    Haro Cases, Jaume; Amorós Torrent, Jaume; Pan, Supriya (springer-Verlag, 2020-05)
    Article
    Open Access
    In 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 ...

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