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Isoperimetric inequalities for Schatten norms of Riesz potentials

Grigori Rozenblioum (Institutionen för matematiska vetenskaper, matematik) ; M. Ruzhansky ; D. Suragan
Journal of Functional Analysis (0022-1236). Vol. 271 (2016), 1, p. 224-239.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Riesz potential, Schatten p-norm, Rayleigh-Faber-Krahn inequality, Hong-Krahn-Szego inequality

Denna post skapades 2016-06-17. Senast ändrad 2016-07-05.
CPL Pubid: 237869


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