• Boundary regularity estimates for nonlocal elliptic equations in C1 and C1, domains 

    Ros-Oton, Xavier; Serra Montolí, Joaquim (2017-02-04)
    Accés obert
    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 ...
  • Boundary regularity for the fractional heat equation 

    Fernández-Real Girona, Xavier (Universitat Politècnica de Catalunya, 2014-09)
    Treball Final de Grau
    Accés obert
    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 ...
  • The Dirichlet problem for the fractional Laplacian: Regularity up to the boundary 

    Ros Oton, Xavier; Serra Montolí, Joaquim (2014-03)
    Accés restringit per política de l'editorial
    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) ...