Invertibility Properties of Singular Integral Operators Associated with the Lamé and Stokes Systems on Infinite Sectors in Two Dimensions
Invertibility Properties of Singular Integral Operators Associated with the Lamé and Stokes Systems on Infinite Sectors in Two Dimensions
复制标题
二维无限扇形上与Lamé和Stokes系统相关的奇异积分算子的可逆性
DOI：
10.1007/s00020-017-2396-4
复制
发表时间：
2017
影响因子：
0.8
通讯作者：
W. Tucker
中科院分区：
文献类型：
--
作者：
I. Mitrea;K. Ott;W. Tucker
本文建立了作用于$$L^p（\partial \Omega）$$Lp（Ω），$$1<p<\infty $$1 <p<∞，当$$\Omega $$Ω是$${\mathbb {R}}^2$$R2中的无限扇形时，弹性静力学和流体静力学的单层和双层势型算子的精确可逆性结果.这一分析与二维曲线多边形类中的Lamé弹性静力学系统和Stokes流体静力学系统的各种边值问题的层势处理有关，例如Dirichlet问题、Neumann问题和正则性问题。梅林变换技术被用来确定这些层电位的可逆性失败的关键可积指数。计算机辅助证明，进一步研究这些指数的单调性属性相对于由部门$$\欧米茄$$Ω的孔径和微分算子的问题。
In this paper we establish sharp invertibility results for the elastostatics and hydrostatics single and double layer potential type operators acting on $$L^p(\partial \Omega )$$Lp(∂Ω), $$1<p<\infty $$1<p<∞, whenever $$\Omega $$Ω is an infinite sector in $${\mathbb {R}}^2$$R2. This analysis is relevant to the layer potential treatment of a variety of boundary value problems for the Lamé system of elastostatics and the Stokes system of hydrostatics in the class of curvilinear polygons in two dimensions, such as the Dirichlet, the Neumann, and the Regularity problems. Mellin transform techniques are used to identify the critical integrability indices for which invertibility of these layer potentials fails. Computer-aided proofs are produced to further study the monotonicity properties of these indices relative to parameters determined by the aperture of the sector $$\Omega $$Ω and the differential operator in question.