Bubbling solutions for nonlocal elliptic problems

  • Juan Dávila

    Universidad de Chile, Santiago, Chile
  • Luis López Ríos

    Universidad de Buenos Aires, Argentina
  • Yannick Sire

    Université Aix-Marseille, France

Abstract

We investigate bubbling solutions for the nonlocal equation

under homogeneous Dirichlet conditions, where is a bounded and smooth domain. The operator stands for two types of nonlocal operators that we treat in a unified way: either the spectral fractional Laplacian or the restricted fractional Laplacian. In both cases , and the Dirichlet conditions are different: for the spectral fractional Laplacian, we prescribe on , and for the restricted fractional Laplacian, we prescribe on . We construct solutions when the exponent is close to the critical one, concentrating as near critical points of a reduced function involving the Green and Robin functions of the domain.

Cite this article

Juan Dávila, Luis López Ríos, Yannick Sire, Bubbling solutions for nonlocal elliptic problems. Rev. Mat. Iberoam. 33 (2017), no. 2, pp. 509–546

DOI 10.4171/RMI/947