A refined result on sign changing solutions for a critical elliptic problem

Yuxin Ge, Monica Musso, Angela Pistoia, Daniel Pollack

Research output: Contribution to journalArticlepeer-review

2 Citations (SciVal)

Abstract

In this work, we consider sign changing solutions to the critical elliptic problem Δu + |u|4/N-2 u = 0 in Ωε and u = 0 on δΩε, where Ωε := Ω-(∪i=1 m (ai +εΩi)) for small parameter ε > 0 is a perforated domain, Ω and Ωi with 0 εΩi (∀i = 1; ⋯ ;m) are bounded regular general domains without symmetry in ℝN and ai are points in Ω for all i = 1; ⋯ ;m. As ε goes to zero, we construct by gluing method solutions with multiple blow up at each point a i for all i = 1; ⋯ ;m.

Original languageEnglish
Pages (from-to)125-155
Number of pages31
JournalCommunications on Pure and Applied Analysis
Volume12
Issue number1
DOIs
Publication statusPublished - 31 Jan 2013

Keywords

  • Critical elliptic problem
  • Green function
  • Multiple blow up

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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