Isoperimetric inequalities for Schatten norms of Riesz potentials
Journal article, 2016

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 R-d. 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-Szego inequalities.

Schatten p-norm

Rayleigh-Faber-Krahn inequality

Hong-Krahn-Szego inequality

Riesz potential


Grigori Rozenblioum

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

M. Ruzhansky

Imperial College London

D. Suragan

Imperial College London

Al Farabi Kazakh National University

Journal of Functional Analysis

0022-1236 (ISSN) 1096-0783 (eISSN)

Vol. 271 1 224-239

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