Invariance of green equilibrium measure on the domain

Research output: Contribution to journalArticle

Abstract

We prove that the Green equilibrium measure and the Green equilibrium energy of a compact set K relative to the domains D and Ω are the same if and only if D is nearly equal to Ω, for a wide class of compact sets K. Also, we prove that equality of Green equilibrium measures arises if and only if the one domain is related with a level set of the Green equilibrium potential of K relative to the other domain.

Original languageEnglish
Pages (from-to)593-600
Number of pages8
JournalFilomat
Volume27
Issue number4
DOIs
StatePublished - 2013

Keywords

  • Equilibrium measure
  • Green capacity
  • Level sets

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