188 Citations
A note on domain monotonicity for the Neumann eigenvalues of the Laplacian
- Mathematics
- 2022
. Given a convex domain and its convex sub-domain we prove a variant of domain monotonicity for the Neumann eigenvalues of the Laplacian. As an application of our method we also obtain an upper bound…
On the bounds of the sum of eigenvalues for a Dirichlet problem involving mixed fractional Laplacians
- MathematicsJournal of Differential Equations
- 2022
Bounds of Dirichlet eigenvalues for Hardy-Leray operator
- Mathematics
- 2021
The purpose of this paper is to study the eigenvalues {λμ,i}i for the Dirichlet Hardy-Leray operator, i.e. −∆u+ μ|x|u = λu in Ω, u = 0 on ∂Ω, where −∆ + μ |x| is the Hardy-Leray operator with μ ≥ −…
Bounds for eigenvalues of the Dirichlet problem for the logarithmic Laplacian
- Mathematics
- 2020
Abstract We provide bounds for the sequence of eigenvalues { λ i ( Ω ) } i {\{\lambda_{i}(\Omega)\}_{i}} of the Dirichlet problem L Δ u = λ u in Ω , u = 0 in ℝ N ∖ Ω ,…
SHARPER ESTIMATES FOR THE EIGENVALUES OF THE DIRICHLET FRACTIONAL LAPLACIAN ON PLANAR DOMAINS
- Mathematics
- 2018
In this article, we study the eigenvalues of the Dirichlet fractional Laplacian operator (−∆)α/2, 0 < α < 1, restricted to a bounded planar domain Ω ⊂ R2. We establish new sharper lower bounds in the…
Maximising Neumann eigenvalues on rectangles. Bulletin of the London Mathematical Society , 48 (5), 877-894.
- Mathematics
- 2016
We obtain results for the spectral optimisation of Neumann eigenvalues on rectangles in R 2 with a measure or perimeter constraint. We show that the rectangle with measure 1 which maximises the k ’th…
Universal Estimates for Eigenvalues and Applications
- Mathematics
- 2016
In this survey, we discuss eigenvalues of the eigenvalue problem of Laplacian. First of all, we consider universal estimates for eigenvalues of the eigenvalue problem of Laplacian. Secondly, as…
A LOWER BOUND FOR EIGENVALUES OF THE POLY-LAPLACIAN WITH ARBITRARY ORDER
- Mathematics
- 2010
We study eigenvalues of the poly-Laplacian of arbitrary order on a bounded domain in an n-dimensional Euclidean space. We obtain a lower bound for these eigenvalues, significantly improving on that…
Dirichlet Eigenvalue Problem of Degenerate Elliptic Operators with Non-Smooth Coefficients
- MathematicsCommunications in Mathematical Research
- 2022
The aim of this review is to introduce some recent results in eigenvalues problems for a class of degenerate elliptic operators with non-smooth coefficients, we present the explicit estimates of the…
Kroger's upper bound types for the Dirichlet eigenvalues of the fractional Laplacian.
- Mathematics
- 2020
We establish an upper bound of the sum of the eigenvalues for the Dirichlet problem of the fractional Laplacian. Our result is obtained by a subtle computation of the Rayleigh quotient for specific…