Stability and approximations of eigenvalues and eigenfunctions of the Neumann Laplacian, part 3

Electronic Journal of Differential Equations

关键词: Stability;    approximations;    Neumann eigenvalues;    and eigenfunctions;   

DOI  :  

来源: DOAJ

【 摘 要 】

This article is a sequel to two earlier articles (one of themwritten jointly with R. Banuelos) on stability results for the Neumanneigenvalues and eigenfunctions of domains in $mathbb{R}^2$ witha snowflake type fractal boundary.In particular we want our results to be applicable to the Koch snowflakedomain. In the two earlier papers we assumed that a domain$Omegasubseteqmathbb{R}^2$ which has a snowflake type boundaryis approximated by a family of subdomains and that the Neumann heatkernel of $Omega$ and those of its approximating subdomains satisfy auniform bound for all sufficiently small t>0. The purpose of thispaper is to extend the results in the two earlier papers to thesituations where the approximating domains are not necessarilysubdomains of $Omega$. We then apply our results to the Koch snowflakedomain when it is approximated from outside by a decreasing sequence ofpolygons.

【 授权许可】

Unknown