Nonexistence of variational minimizers related to a quasilinear singular problem in metric measure spaces

PRASHANTA GARAIN*, JUHA KINNUNEN

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

In this article we consider a variational problem related to a quasilinear singular problem and obtain a nonexistence result in a metric measure space with a doubling measure and a Poincaré inequality. Our method is purely variational and to the best of our knowledge, this is the first work concerning singular problems in a general metric setting.

Original languageEnglish
Pages (from-to)3407-3416
Number of pages10
JournalProceedings of the American Mathematical Society
Volume149
Issue number8
DOIs
Publication statusPublished - Aug 2021
MoE publication typeA1 Journal article-refereed

Keywords

  • Analysis on metric measure spaces
  • Energy estimate
  • Minimizer
  • Newtonian space
  • Nonexistence
  • Variational integral

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