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Related papers: Trace and inverse trace of Steklov eigenvalues

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This is a continuation of our previous work arXiv:1601.05617 on trace and inverse trace of Steklov eigenvalues. More new inequalities for the trace and inverse trace of Steklov eigenvalues are obtained.

Differential Geometry · Mathematics 2016-09-02 Yongjie Shi , Chengjie Yu

In this paper, motivated by the work of Raulot and Savo, we generalize Raulot-Savo's estimate for the first Steklov eigenvalues of Euclidean domains to higher Steklov eigenvalues.

Differential Geometry · Mathematics 2017-04-05 Liangwei Yang , Chengjie Yu

In this paper, we generalize the Hersch-Payne-Schiffer inequality for Steklov eigenvalues to higher dimensional case by extending the trick used by Hersch, Payne and Schiffer to higher dimensional manifolds.

Differential Geometry · Mathematics 2015-08-26 Liangwei Yang , Chengjie Yu

We give explicit isoperimetric upper bounds for all Steklov eigenvalues of a compact orientable surface with boundary, in terms of the genus, the length of the boundary, and the number of boundary components. Our estimates generalize a…

Spectral Theory · Mathematics 2013-10-10 Alexandre Girouard , Iosif Polterovich

We prove generalized Cheeger inequalities for eigenvalues of Laplacians for reversible Markov chains. Then we apply Hassannezhad and Miclo's convergence result to obtain Jammes Cheeger inequalities for Steklov eigenvalues. In particular, we…

Differential Geometry · Mathematics 2025-09-09 Bobo Hua , Supanat Kamtue , Shiping Liu , Florentin Münch , Norbert Peyerimhoff

In this short note, we show the rigidity of a trace estimate for Steklov eigenvalues with respect to functions in our previous work (Trace and inverse trace of Steklov eigenvalues. J. Differential Equations 261 (2016), no. 3, 2026--2040.).…

Differential Geometry · Mathematics 2020-01-22 Yongjie Shi , Chengjie Yu

A recent area of interest is the development and study of eigenvalue problems arising in scattering theory that may provide potential target signatures for use in nondestructive testing of materials. We consider a generalization of the…

Analysis of PDEs · Mathematics 2020-07-01 Samuel Cogar

In this paper, we obtain a Lichnerowicz-type estimate for the first Steklov eigenvalues on graphs and discuss its rigidity.

Differential Geometry · Mathematics 2020-10-28 Yongjie Shi , Chengjie Yu

In this paper, we study the upper bounds for discrete Steklov eigenvalues on trees via geometric quantities. For a finite tree, we prove sharp upper bounds for the first nonzero Steklov eigenvalue by the reciprocal of the size of the…

Spectral Theory · Mathematics 2022-03-10 Zunwu He , Bobo Hua

We study convexity or concavity of certain trace functions for the deformed logarithmic and exponential functions, and obtain in this way new trace inequalities for deformed exponentials that may be considered as generalizations of…

Mathematical Physics · Physics 2017-08-02 Frank Hansen , Jin Liang , Guanghua Shi

In this paper, we extend a lower bound estimate for Steklov eigenvalues by Perrin \cite{Pe} on unit-weighted graphs to general weighted graphs and characterise its rigidity.

Spectral Theory · Mathematics 2025-04-11 Yongjie Shi , Chengjie Yu

In this paper, we obtain monotonicity of Steklov eigenvalues on graphs which as a special case on trees extends the results of He-Hua [Calc. Var. Partial Differential Equations 61 (2022), no. 3, Paper No. 101, arXiv: 2103.07696] to higher…

Differential Geometry · Mathematics 2022-05-16 Chengjie Yu , Yingtao Yu

This paper proposes and analyzes an a posteriori error estimator for the finite element multi-scale discretization approximation of the Steklov eigenvalue problem. Based on the a posteriori error estimates, an adaptive algorithm of shifted…

Numerical Analysis · Mathematics 2016-01-08 Hai Bi , Hao Li , Yidu Yang

In this paper, we consider the numerical approximation of the Steklov eigenvalue problem that arises in inverse acoustic scattering. The underlying scattering problem is for an inhomogeneous isotropic medium. These eigenvalues have been…

Analysis of PDEs · Mathematics 2021-04-21 Isaac Harris

The Steklov eigenvalue problem, first introduced over 125 years ago, has seen a surge of interest in the past few decades. This article is a tour of some of the recent developments linking the Steklov eigenvalues and eigenfunctions of…

Spectral Theory · Mathematics 2023-09-06 Bruno Colbois , Alexandre Girouard , Carolyn Gordon , David Sher

We consider Steklov eigenvalues of nearly circular domains in $\R^{2}$ of fixed unitary area. In \cite{viator2018}, the authors treated such domains as perturbations of the disk, and they computed the first-order term of the asymptotic…

Analysis of PDEs · Mathematics 2025-05-01 Lucas Alland , Robert Viator

Considering potentials defined by Bessel kernel with Bessel convolution a Kerman-Sawyer type characterization of trace inequality is given. As an application an estimate on the least eigenvalue of Schr\"odinger-Bessel operators is derived.

Classical Analysis and ODEs · Mathematics 2024-09-30 Mouna Chegaar , Á. P. Horváth

We explore the Steklov eigenvalue problem on convex polygons, focusing mainly on the inverse Steklov problem. Our primary finding reveals that, for almost all convex polygonal domains, there exist at most finitely many non-congruent domains…

Spectral Theory · Mathematics 2024-08-06 Emily B. Dryden , Carolyn Gordon , Javier Moreno , Julie Rowlett , Carlos Villegas-Blas

We prove a Cheeger inequality for the first positive Steklov eigenvalue. It involves two isoperimetric constants.

Differential Geometry · Mathematics 2015-09-30 Pierre Jammes

We introduce the biharmonic Steklov problem on differential forms by considering suitable boundary conditions. We characterize its smallest eigenvalue and prove elementary properties of the spectrum. We obtain various estimates for the…

Differential Geometry · Mathematics 2022-06-13 Fida El Chami , Nicolas Ginoux , Georges Habib , Ola Makhoul
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