Isoperimetric inequalities for Schatten norms of Riesz potentials

G. Rozenblum, M. Ruzhansky, D. Suragan

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

In this note we prove that the ball is a maximiser for integer order Schatten p-norms of the Riesz potential operators among all domains of a given measure in Rd. In particular, the result is valid for the polyharmonic Newton potential operator, which is related to a nonlocal boundary value problem for the poly-Laplacian extending the one considered by M. Kac in the case of the Laplacian, so we obtain isoperimetric inequalities for its eigenvalues as well, namely, analogues of Rayleigh-Faber-Krahn and Hong-Krahn-Szegö inequalities.

Original languageEnglish
Pages (from-to)224-239
Number of pages16
JournalJournal of Functional Analysis
Volume271
Issue number1
DOIs
Publication statusPublished - Jul 1 2016

Keywords

  • Hong-Krahn-Szegö inequality
  • Rayleigh-Faber-Krahn inequality
  • Riesz potential
  • Schatten p-norm

ASJC Scopus subject areas

  • Analysis

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