Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6415011 | Journal of Functional Analysis | 2016 | 16 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
G. Rozenblum, M. Ruzhansky, D. Suragan,