Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6417542 | Journal of Mathematical Analysis and Applications | 2016 | 14 Pages |
Abstract
In this paper we prove that the disc is a maximiser of the Schatten p-norm of the logarithmic potential operator among all domains of a given measure in R2, for all even integers 2â¤p<â. We also show that the equilateral triangle has the largest Schatten p-norm among all triangles of a given area. For the logarithmic potential operator on bounded open or triangular domains, we also obtain analogies of the Rayleigh-Faber-Krahn or Pólya inequalities, respectively. The logarithmic potential operator can be related to a nonlocal boundary value problem for the Laplacian, so we obtain isoperimetric inequalities for its eigenvalues as well.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Michael Ruzhansky, Durvudkhan Suragan,