Now showing items 1-5 of 5

  • Boundary regularity for the fractional heat equation 

    Fernández-Real Girona, Xavier (Universitat Politècnica de Catalunya, 2014-09)
    Bachelor thesis
    Open Access
    In this dissertation we present an introduction to nonlocal operators, and in particular, we study the fractional heat equation, which involves the fractional Laplacian of order 2s. In the first chapters we make a review ...
  • Layer solutions for the fractional Laplacian on hyperbolic space: existence, uniqueness and qualitative properties 

    González Nogueras, María del Mar; Saéz, Mariel; Sire, Yannick (2014-12-01)
    Article
    Restricted access - publisher's policy
    We investigate the equation; (-Delta(Hn))(gamma) w = f(w) in H-n,; where (-Delta(Hn))(gamma) corresponds to the fractional Laplacian on hyperbolic space for gamma is an element of(0, 1) and f is a smooth nonlinearity that ...
  • Local integration by parts and Pohozaev indentities for higuer order fractional Laplacians 

    Ros Oton, Xavier; Serra Montolí, Joaquim (2015-05-01)
    Article
    Restricted access - publisher's policy
    We establish an integration by parts formula in bounded domains for the higher order fractional Laplacian (-Delta)(s) with s > 1. We also obtain the Pohozaev identity for this operator. Both identities involve local boundary ...
  • Positive solutions of nonlinear problems involving the square root of the Laplacian 

    Cabré Vilagut, Xavier; Tan, Jinggang (2009-05)
    External research report
    Open Access
    We consider nonlinear elliptic problems involving a nonlocal operator: the square root of the Laplacian in a bounded domain with zero Dirichlet boundary conditions. For positive solutions to problems with power nonlinearities, ...
  • The Dirichlet problem for the fractional Laplacian: Regularity up to the boundary 

    Ros Oton, Xavier; Serra Montolí, Joaquim (2014-03)
    Article
    Restricted access - publisher's policy
    We study the regularity up to the boundary of solutions to the Dirichlet problem for the fractional Laplacian. We prove that if u is a solution of (-d)su=g in O, u=0 in Rn\O, for some s¿(0, 1) and g¿L8(O), then u is Cs(Rn) ...