27 citations · 95 across the 24 of their papers we have counts for
3 papers · 2 filters
Shape optimization for low Neumann and Steklov eigenvalues
Alexandre Girouard, Iosif Polterovich
We give an overview of results on shape optimization for low eigenvalues of the Laplacian on bounded planar domains with Neumann and Steklov boundary conditions. These results shar…
On the Hersch-Payne-Schiffer inequalities for Steklov eigenvalues
Alexandre Girouard, Iosif Polterovich
We prove that the isoperimetric inequality due to Hersch-Payne-Schiffer for the n-th nonzero Steklov eigenvalue of a bounded simply-connected planar domain is sharp for all n=1,2,.…
Maximization of the second positive Neumann eigenvalue for planar domains
Alexandre Girouard, Nikolai Nadirashvili, Iosif Polterovich
We prove that the second positive Neumann eigenvalue of a bounded simply-connected planar domain of a given area does not exceed the first positive Neumann eigenvalue on a disk of…