Les Equacions en Derivades Parcials, EDPs, són una de las eines fonamentals de la modelització matemàtica en Biologia, Física, Química, Economia i Indústria. El seu estudi analític i les seves aplicacions formen l'eix del grup de recerca. El nostre interés central són les EDPs no lineals amb difusió standard o fraccionària i les EDPs de primer ordre amb termes no-locals. Estudiem el seu orígen i aplicacions en problemes de reacció, en biologia matemàtica, dinàmica de poblacions, problemes geomètrics, dinàmica d'ones, i models de formació de preus.

http://futur.upc.edu/EDP

Enviaments recents

  • Boundedness of stable solutions to semilinear elliptic equations: A survey 

    Cabré Vilagut, Xavier (2017-05-01)
    Article
    Accés obert
    This article is a survey on boundedness results for stable solutions to semilinear elliptic problems. For these solutions, we present the currently known L8 estimates that hold for all nonlinearities. Such estimates are ...
  • Boundary regularity estimates for nonlocal elliptic equations in C1 and C1, domains 

    Ros-Oton, Xavier; Serra Montolí, Joaquim (2017-02-04)
    Article
    Accés restringit per política de l'editorial
    We establish sharp boundary regularity estimates in C1 and C1,a domains for nonlocal problems of the form Lu=f in O, u=0 in Oc. Here, L is a nonlocal elliptic operator of order 2s, with s¿(0,1). First, in C1,a domains we ...
  • Dirac operators, shell interactions, and discontinuous gauge functions across the boundary 

    Mas Blesa, Albert (2017-02-01)
    Article
    Accés obert
    Given a bounded smooth domain Ω ⊂ R3, we explore the relation between couplings of the free Dirac operator −iα · ∇ + mβ with pure electrostatic shell potentials λδ∂Ω (λ ∈ R) and some perturbations of those potentials given ...
  • Differentiability with respect to parameters in global smooth linearization 

    Rodrigues, Hildebrando M.; Solà-Morales Rubió, Joan de (2017-03-15)
    Article
    Accés restringit per política de l'editorial
    Let XX be a Banach space and T¿:X¿XT¿:X¿X a family of invertible contractions, T¿=L¿+f¿T¿=L¿+f¿, where L¿L¿ is linear and f¿f¿ is nonlinear with f¿(0)=0f¿(0)=0. We give conditions for the existence of a family of global ...
  • Teleparallel loop quantum cosmology in a system of intersecting branes 

    Haro Cases, Jaume (Elsevier, 2016-09-10)
    Article
    Accés restringit per política de l'editorial
    Recently, some authors have removed the big bang singularity in teleparallel Loop Quantum Cosmology (LQC) and have shown that the universe may undergo a number of oscillations. We investigate the origin of this type of ...
  • Evolution and dynamics of a matter creation model 

    Pan, Supriya; Haro Cases, Jaume; Paliathanasis, A.; Slagter, R.J. (2016-05-01)
    Article
    Accés obert
    In a flat Friedmann–Lemaître–Robertson–Walker (FLRW) geometry, we consider the expansion of the universe powered by the gravitationally induced ‘adiabatic’ matter creation. To demonstrate how matter creation works well ...
  • Gravitationally induced adiabatic particle production: from big bang to de Sitter 

    Haro Cases, Jaume (2016-07-27)
    Article
    Accés restringit per política de l'editorial
    In the background of a flat homogeneous and isotropic space–time, we consider a scenario of the Universe driven by the gravitationally induced 'adiabatic' particle production with constant creation rate. We have shown that ...
  • Isoperimetric, Sobolev, and eigenvalue inequalities via the Alexandroff-Bakelman-Pucci method: A survey 

    Cabré Vilagut, Xavier (2017-01-05)
    Article
    Accés restringit per política de l'editorial
    This paper presents the proof of several inequalities by using the technique introduced by Alexandroff, Bakelman, and Pucci to establish their ABP estimate. First, the author gives a new and simple proof of a lower bound ...
  • Sharp isoperimetric inequalities via the ABP 

    Cabré Vilagut, Xavier; Ros-Oton, Xavier; Serra, Joaquim (2016-01-01)
    Article
    Accés obert
    Given an arbitrary convex cone of Rn, we find a geometric class of homogeneous weights for which balls centered at the origin and intersected with the cone are minimizers of the weighted isoperimetric problem in the convex ...
  • Simple inflationary quintessential model. II. Power law potentials 

    Haro Cases, Jaume; Amorós Torrent, Jaume; Pan, Supriya (American Physical Society, 2016-09-21)
    Article
    Accés obert
    The present work is a sequel of our previous work [Phys. Rev. D 93, 084018 (2016)] which depicted a simple version of an inflationary quintessential model whose inflationary stage was described by a Higgs-type potential ...

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