Now showing items 1-12 of 12

  • An extension problem for sums of fractional Laplacians and 1-D symmetry of phase transitions 

    Cabré Vilagut, Xavier; Serra Montolí, Joaquim (2015-09-10)
    Article
    Open Access
    We study nonlinear elliptic equations for operators corresponding to non-stable Lévy diffusions. We include a sum of fractional Laplacians of different orders. Such operators are infinitesimal generators of non-stable ...
  • Boundary regularity estimates for nonlocal elliptic equations in C1 and C1, domains 

    Ros-Oton, Xavier; Serra Montolí, Joaquim (2017-02-04)
    Article
    Open Access
    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 ...
  • C sigma+alfa regularity for concave nonlocal fully nonlinear elliptic equations with rough kernels 

    Serra Montolí, Joaquim (2015-12-01)
    Article
    Open Access
    We establish Cs+a interior estimates for concave nonlocal fully nonlinear equations of order s¿(0,2) with rough kernels. Namely, we prove that if u¿Ca(Rn) solves in B1 a concave translation invariant equation with kernels ...
  • Elliptic and parabolic PDEs : regularity for nonlocal diffusion equations and two isoperimetric problems 

    Serra Montolí, Joaquim (Universitat Politècnica de Catalunya, 2014-06-17)
    Doctoral thesis
    Open Access
    The thesis is divided into two parts. The first part is mainly concerned with regularity issues for integro-differential (or nonlocal) elliptic and parabolic equations. In the same way that densities of particles with ...
  • Fractional Laplacian: Pohozaev identity and nonexistence results 

    Ros Oton, Xavier; Serra Montolí, Joaquim (Elsevier, 2012-05)
    Article
    Restricted access - publisher's policy
    In this Note we present the Pohozaev identity for the fractional Laplacian. As a consequence of this identity, we prove the nonexistence of nontrivial bounded solutions to semilinear problems with supercritical nonlinearities ...
  • 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 ...
  • Nonexistence results for nonlocal equations with critical and supercritical nonlinearities 

    Ros Oton, Xavier; Serra Montolí, Joaquim (2015-01-02)
    Article
    Open Access
    We prove nonexistence of nontrivial bounded solutions to some nonlinear problems involving nonlocal operators of the form; [GRAPHICS]; These operators are infinitesimal generators of symmetric Levy processes. Our results ...
  • Pohozaev identities for anisotropic integrodifferential operators 

    Ros Oton, Xavier; Serra Montolí, Joaquim; Valdinoci, Enrico (2017-08-15)
    Article
    Open Access
    We find and prove new Pohozaev identities and integration by parts type formulas for anisotropic integrodifferential operators of order 2s, with s¿(0,1). These identities involve local boundary terms, in which the quantity ...
  • Radial symmetry of solutions to diffusion equations with discontinuous nonlinearities 

    Serra Montolí, Joaquim (2013-02-15)
    Article
    Restricted access - publisher's policy
    We prove a radial symmetry result for bounded nonnegative solutions to the p-Laplacian semilinear equation −Δpu=f(u) posed in a ball of Rn and involving discontinuous nonlinearities f. When p=2 we obtain a new result which ...
  • 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) ...
  • The extremal solution for the fractional Laplacian 

    Ros Oton, Xavier; Serra Montolí, Joaquim (2014-07-01)
    Article
    Restricted access - publisher's policy
    We study the extremal solution for the problem (-¿)su=¿f(u) in O , u=0 in Rn\O , where ¿>0 is a parameter and s¿(0,1) . We extend some well known results for the extremal solution when the operator is the Laplacian to this ...
  • The Pohozaev identity for the fractional Laplacian 

    Ros Oton, Xavier; Serra Montolí, Joaquim (2014-08-01)
    Article
    Open Access
    In this paper we prove the Pohozaev identity for the semilinear Dirichlet problem (-Delta)(s) u = f(u) in Omega, u equivalent to 0 in R-n\Omega. Here, s is an element of (0, 1), (-Delta)(s) is the fractional Laplacian in ...