A direct method of moving spheres on fractional order equations

Wenxiong Chen, Yan Li, Ruobing Zhang

Research output: Contribution to journalArticlepeer-review

37 Scopus citations

Abstract

In this paper, we introduce a direct method of moving spheres for the fractional Laplacian (−△)α/2 with 0>α>2, in which a key ingredient is the narrow region maximum principle. As immediate applications, we classify non-negative solutions for semilinear equations involving the fractional Laplacian in Rn; we prove a non-existence result for the prescribing Qα curvature equation on Sn; then by combining the direct method of moving planes and moving spheres, we establish a Liouville type theorem on a half Euclidean space. We expect to see more applications of this method to many other nonlinear equations involving non-local operators.

Original languageEnglish (US)
Pages (from-to)4131-4157
Number of pages27
JournalJournal of Functional Analysis
Volume272
Issue number10
DOIs
StatePublished - May 15 2017

All Science Journal Classification (ASJC) codes

  • Analysis

Keywords

  • Direct method of moving spheres
  • Fractional Laplacians
  • Non-existence of solutions
  • Radial symmetry

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