DOI

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.

Язык оригиналаанглийский
Страницы (с-по)224-239
Число страниц16
ЖурналJournal of Functional Analysis
Том271
Номер выпуска1
DOI
СостояниеОпубликовано - 1 июл 2016

    Предметные области Scopus

  • Анализ

ID: 50650350