Search results for "Neumann eigenvalues"
showing 3 items of 3 documents
Sharp estimates for eigenfunctions of a Neumann problem
2009
In this paper we provide some bounds for the eigenfunctions of the Laplacian with homogeneous Neumann boundary conditions in a bounded domain Ω of R^n. To this aim we use the so-called symmetrization techniques and the obtained estimates are asymptotically sharp, at least in the bidimensional case, when the isoperimetric constant relative to Ω goes to 0.
The equality case in a Poincaré–Wirtinger type inequality
2016
It is known that, for any convex planar set W, the first non-trivial Neumann eigenvalue μ1 (Ω) of the Hermite operator is greater than or equal to 1. Under the additional assumption that Ω is contained in a strip, we show that β1 (Ω) = 1 if and only if Ω is any strip. The study of the equality case requires, among other things, an asymptotic analysis of the eigenvalues of the Hermite operator in thin domains.
A sharp estimate for Neumann eigenvalues of the Laplace-Beltrami operator for domains in a hemisphere
2018
Here, we prove an isoperimetric inequality for the harmonic mean of the first [Formula: see text] non-trivial Neumann eigenvalues of the Laplace–Beltrami operator for domains contained in a hemisphere of [Formula: see text].