Balls Minimize Moments of Logarithmic and Newtonian Equilibrium Measures

Carrie Clark, Richard S. Laugesen

Research output: Contribution to journalArticlepeer-review

Abstract

The q-th moment (q>0) of electrostatic equilibrium measure is shown to be minimal for a centered ball among 3-dimensional sets of given capacity, while among 2-dimensional sets a centered disk is the minimizer for 0<q≤2. Analogous results are developed for Newtonian capacity in higher dimensions and logarithmic capacity in 2 dimensions. Open problems are raised for Riesz equilibrium moments.

Original languageEnglish (US)
JournalPotential Analysis
DOIs
StateAccepted/In press - 2024

Keywords

  • 31B15
  • Electrostatic
  • Potential theory
  • Primary 31A15
  • Riesz capacity
  • Secondary 35B51

ASJC Scopus subject areas

  • Analysis

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