关于窄缝区域上Laplace方程Neumann问题的谱
On the spectrum of the Neumann problem for Laplace equation in a domain with a narrow slit
摘要：
研究了二维区域中带狭缝的Neumann问题。狭缝的宽度是一个小参数。利用匹配渐近展开法构造了摄动问题特征值收敛于极限问题简单特征值的完全渐近展开式。它表明，经常扰动理论可以正式应用在一个自然的方式，以条款的顺序$ε^2$。然而，这样得到的结果是错误的。正确的结果只能通过内渐近展开式得到。
英文摘要：
The Neumann problem in two-dimensional domain with a narrow slit is studied. The width of the slit is a small parameter. The complete asymptotic expansion for the eigenvalue of the perturbed problem converging to a simple eigenvalue of the limiting problem is constructed by means of the method of the matched asymptotic expansions. It is shown that the regular perturbation theory can formally be applied in a natural way up to terms of order $ε^2$. However, the result obtained in that way is false. The correct result can be obtained only by means of inner asymptotic expansion.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
