• Positive solutions of nonlinear problems involving the square root of the Laplacian 

      Cabré Vilagut, Xavier; Tan, Jinggang (2009-05)
      Report de recerca
      Accés obert
      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, ...
    • Regularity of stable solutions to reaction-diffusion elliptic equations 

      Cabré Vilagut, Xavier (European Mathematical Society Press, 2023-07-14)
      Capítol de llibre
      Accés obert
      The boundedness of stable solutions to semilinear (or reaction-diffusion) elliptic PDEs has been studied since the 1970s. In dimensions 10 and higher, there exist stable energy solutions which are unbounded (or singular). ...