On an interior Calderón operator and a related Steklov eigenproblem for Maxwell's equations

广义特征值问题与具有非线性边界条件的nonlinear elliptic系统

Generalized eigenproblem and nonlinear elliptic system with nonlinear boundary conditions

本文主要研究具有非线性边界条件的二阶椭圆型偏微分方程组的可解性。我们研究了广义Steklov Robin特征系统（可能有矩阵权），其中谱参数既在系统中又在边界上。当微分系统中的非线性项和边界上的非线性项在某种意义下与Steklov Robin的广义谱相互作用时，证明了非线性系统解的存在性.证明方法利用了勒雷-绍德尔度。

延拓域上的Poincaré-Steklov算子与Calderón问题

Poincar{é}-Steklov operator and Calder{ó}n's problem on extension domains

本文在包含非Lipschitz和分形形状的Sobolev延拓域上推广Poincaré-Steklov算子，证明正问题稳定性，并利用边界稳定性在n≥3时识别Lipschitz电导率及边界附近为常数的W^{2,∞}电导率。

On a Steklov spectrum in Electromagnetics

After presenting various concepts and results concerning the classical Steklov eigenproblem, we focus on analogous problems for time-harmonic Maxwell's equations in a cavity. In this direction, we discuss recent rigorous results concerning natural Steklov boundary value problems for the curlcurl operator. Moreover, we explicitly compute eigenvalues and eigenfunctions in the unit ball of the three-dimensional Euclidean space by using classical vector spherical harmonics.

径向薛定谔算子的逆 Steklov 与 Calderón 问题中的局部 Hölder 稳定性及量化共振

Local Hölder Stability in the Inverse Steklov and Calderón Problems for Radial Schrödinger operators and Quantified Resonances

本文针对单位球上特殊 $L^2$ 径向势的薛定谔算子，利用 Steklov 频谱差的 Laplace 变换公式与矩稳定性估计，获得了逆 Steklov 与 Calderón 问题的局部 Hölder 稳定性，改进了先前的对数稳定性结果。

Steklov eigenvalues for the Lamé operator in linear elasticity

In this paper we study Steklov eigenvalues for the Lamé operator which arise in the theory of linear elasticity. In this eigenproblem the spectral parameter appears in a Robin boundary condition, linking the traction and the displacement. To establish the existence of a countable spectrum for this problem, we present an extension of Korn's inequality. We also show that a proposed conforming Galerkin scheme provides convergent approximations to the true eigenvalues. A standard finite element method is used to conduct numerical experiments on 2D and 3D domains to support our theoretical findings…

Stability estimates for an inverse Steklov problem in a class of hollow spheres

In this paper, we study an inverse Steklov problem in a class of n-dimensional manifolds having the topology of a hollow sphere and equipped with a warped product metric. Precisely, we aim at studying the continuous dependence of the warping function dening the warped product with respect to the Steklov spectrum. We first show that the knowledge of the Steklov spectrum up to an exponential decreasing error is enough to determine uniquely the warping function in a neighbourhood of the boundary. Second, when the warping functions are symmetric with respect to 1/2, we prove a log-type stability e…