• Energy estimates and 1-D symmetry for nonlinear equations involving the half-Laplacian 

      Cabré Vilagut, Xavier; Cinti, Eleonora (2010-11)
      Article
      Accés restringit per política de l'editorial
      We establish sharp energy estimates for some solutions, such as global minimizers, monotone solutions and saddle-shaped solutions, of the fractional nonlinear equation 1/2 in R n. Our energy estimates hold for every ...
    • Sharp energy estimates for nonlinear fractional diffusion equations 

      Cabré Vilagut, Xavier; Cinti, Eleonora (2014-01)
      Article
      Accés restringit per política de l'editorial
      We study the nonlinear fractional equation (−Δ)su=f(u) in Rn, for all fractions 0<s<1 and all nonlinearities f . For every fractional power s∈(0,1) , we obtain sharp energy estimates for bounded global minimizers and for ...
    • Stable s-minimal cones in R 3 are flat for s ~ 1 

      Cabré Vilagut, Xavier; Cinti, Eleonora; Serra, Joaquim (2019-01-01)
      Article
      Accés obert
      We prove that half spaces are the only stable nonlocal s-minimal cones in R3, for s¿(0,1) sufficiently close to 1. This is the first classification result of stable s-minimal cones in dimension higher than two. Its proof ...