椭圆算子的精确边界估计

高阶椭圆算子谱稳定性的精确估计（基于区域的勒贝格测度）

Sharp spectral stability estimates via the Lebesgue measure of domains for higher order elliptic operators

我们证明了尖锐的稳定性估计的变化的特征值的任意偶数阶的非负自伴椭圆算子的变化的开放集上，他们被定义。这些估计用开集的对称差的勒贝格测度表示。Dirichlet和Neumann边界条件。

Addendum to 'The equivariant spectral function of an invariant elliptic operator'

Let $M$ be a compact boundaryless Riemannian manifold, carrying an effective and isometric action of a torus $T$, and $P_0$ an invariant elliptic classical pseudodifferential operator on $M$. In this note, we strengthen asymptotics for the equivariant (or reduced) spectral function of $P_0$ derived previously, which are already sharp in the eigenvalue aspect, to become almost sharp in the isotypic aspect. In particular, this leads to hybrid equivariant $L^p$-bounds for eigenfunctions that are almost sharp in the eigenvalue and isotypic aspect.

Boundary integral formulations of eigenvalue problems for elliptic differential operators with singular interactions and their numerical approximation by boundary element methods

In this paper the discrete eigenvalues of elliptic second order differential operators in $L^2(\mathbb{R}^n)$, $n \in \mathbb{N}$, with singular $δ$- and $δ'$-interactions are studied. We show the self-adjointness of these operators and derive equivalent formulations for the eigenvalue problems involving boundary integral operators. These formulations are suitable for the numerical computations of the discrete eigenvalues and the corresponding eigenfunctions by boundary element methods. We provide convergence results and show numerical examples.

四阶椭圆型方程解的边界衰减估计

Boundary decay estimates for solutions of fourth-order elliptic equations

得到了具有正则边界的有界区域上四阶椭圆型方程解的积分边界衰减估计。我们应用这些估计，以获得相应的特征值的边界小扰动下的稳定性界限。

具有不同边界条件的拟线性椭圆型方程的Eigenvalue均匀化

Eigenvalue homogenization for quasilinear elliptic equations with different boundary conditions

研究了有界区域内几类含振荡权的非线性问题在不同边界条件下特征值的（变分）收敛速度收敛速率。

锥流形上椭圆边值问题的解

Resolvents of elliptic boundary problems on conic manifolds

本文是对Math.AP/0410178和Math.AP/0410176中关于锥流形上椭圆算子的预解式的研究的继续，并推广到了有边流形的情形和算子在边界条件下的实现。在符号上的自然椭圆性条件下，证明了锥算子边值问题实现的最小增长扇区的存在性。特别注意致力于澄清的解析结构的预解式。