Related papers: Trace and inverse trace of Steklov eigenvalues II

In this paper, we obtain some new estimates for the trace and inverse trace of Steklov eigenvalues. The estimates generalize some previous results of Hersch-Payne-Schiffer , Brock}, Raulot-Savo and Dittmar.

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…

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…

In this paper, we obtain some new inequalities for functions whose second derivatives' absolute value is s-convex and log-convex. Also, we give some applications for numerical integration.

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.).…

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…

In these notes, we present versions of trace theorems for Sobolev spaces over an interval in the real line, and also a one-dimensional version of the well-known Poincare inequality.

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

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…

Some new inequalities of Ostrowski type for twice differentiable mappings whose derivatives in absolute value are s-convex in the second sense are given.Applications for special means are also provided.

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…

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.

In this paper, we obtain some companions of Ostrowski type inequality for absolutely continuous functions whose second derivatives absolute value are s-convex and s-concave.

Sobolev trace inequalities on nonhomogeneous fractional Sobolev spaces are established.

In this paper, we obtained some new Ostrowski-Gruss type inequalities contains twice differentiable functions.

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…

We establish a fourth order sharp Sobolev trace inequality on three-balls, and its equivalence to a third order sharp Sobolev inequality on two-spheres.

We provide a new characterization of the logarithmic Sobolev inequality.

This paper studies the inverse Steklov spectral problem for curvilinear polygons. For generic curvilinear polygons with angles less than $\pi$, we prove that the asymptotics of Steklov eigenvalues obtained in arXiv:1908.06455 determines, in…

The goal of this review is to explain some recent results regarding generalizations of the Stein-Tomas (and Strichartz) inequalities to the context of trace ideals (Schatten spaces).