Isoperimetric inequalities for Schatten norms of Riesz potentials
Artikel i vetenskaplig tidskrift, 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

Hong-Krahn-Szego inequality

Rayleigh-Faber-Krahn inequality

Riesz potential


Grigori Rozenblioum

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

M. Ruzhansky

Imperial College London

D. Suragan

Al Farabi Kazakh National University, Institute of Mathematics and Mathematical Modeling

Imperial College London

Journal of Functional Analysis

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

Vol. 271 224-239