[HTML][HTML] Isoperimetric inequalities for Schatten norms of Riesz potentials
Journal of Functional Analysis, 2016•Elsevier
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–Szegö inequalities.
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–Szegö inequalities.
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–Szegö inequalities.
Elsevier
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