Inequalities for the Steklov eigenvalues

On Principal Eigenvalues for Periodic Parabolic Steklov Problems

LetΩ be aC2+γ domain in RN ,N ≥ 2, 0 < γ < 1. LetT>0 and let L be a uniformly parabolic operator Lu= ∂u/∂t−∑i, j(∂/∂xi)(ai j(∂u/∂xj)) +∑ j b j(∂u/∂xi) + a0u, a0 ≥ 0, whose coefficients, depending on (x, t) ∈Ω×R, are T periodic in t and satisfy some regularity assumptions. Let A be the N ×N matrix whose i, j entry is ai j and let ν be the unit exterior normal to ∂Ω. Let m be a T-periodic functio...

Two-Parameter Eigenvalues Steklov Problem involving the p-Laplacian

We study the existence of eigenvalues for a two parameter Steklov eigenvalues problem with weights. Moreover, we prove the simplicity and the isolation results of the principal eigenvalue. Finally, we obtain the continuity and the differentiability of this principal eigenvalue. AMS Subject Classifications: 35J60, 35B33.

Sloshing, Steklov and corners I: Asymptotics of sloshing eigenvalues

This is the first in a series of two papers aiming to establish sharp spectral asymptotics for Steklov type problems on planar domains with corners. In the present paper we focus on the two-dimensional sloshing problem, which is a mixed Steklov-Neumann boundary value problem describing small vertical oscillations of an ideal fluid in a container or in a canal with a uniform cross-section. We pr...

Isoperimetric Inequalities and Eigenvalues

Isoperimetric Inequalities and Eigenvalues

An upper bound is given on the minimum distance between i subsets of the same size of a regular graph in terms of the i-th largest eigenvalue in absolute value. This yields a bound on the diameter in terms of the i-th largest eigenvalue, for any integer i. Our bounds are shown to be asymptotically tight. A recent result by Quenell relating the diameter, the second eigenvalue, and the girth of a...