Stability and approximations of eigenvalues and eigenfunctions of the Neumann Laplacian, part 3
This article is a sequel to two earlier articles (one of them written jointly with R. Banuelos) on stability results for the Neumann eigenvalues and eigenfunctions of domains in $mathbb{R}^2$ with a snowflake type fractal boundary. In particular we want our results to be applicable to the Koch s...
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| Format: | Article |
| Language: | English |
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Texas State University
2011-08-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2011/100/abstr.html |
| _version_ | 1818938917942984704 |
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| author | Michael M. H. Pang |
| author_facet | Michael M. H. Pang |
| author_sort | Michael M. H. Pang |
| collection | DOAJ |
| description | This article is a sequel to two earlier articles (one of them written jointly with R. Banuelos) on stability results for the Neumann eigenvalues and eigenfunctions of domains in $mathbb{R}^2$ with a snowflake type fractal boundary. In particular we want our results to be applicable to the Koch snowflake domain. In the two earlier papers we assumed that a domain $Omegasubseteqmathbb{R}^2$ which has a snowflake type boundary is approximated by a family of subdomains and that the Neumann heat kernel of $Omega$ and those of its approximating subdomains satisfy a uniform bound for all sufficiently small t>0. The purpose of this paper is to extend the results in the two earlier papers to the situations where the approximating domains are not necessarily subdomains of $Omega$. We then apply our results to the Koch snowflake domain when it is approximated from outside by a decreasing sequence of polygons. |
| first_indexed | 2024-12-20T06:15:29Z |
| format | Article |
| id | doaj.art-c3eb4822702342b19c3357f6a066784d |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-20T06:15:29Z |
| publishDate | 2011-08-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-c3eb4822702342b19c3357f6a066784d2022-12-21T19:50:33ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912011-08-012011100,154Stability and approximations of eigenvalues and eigenfunctions of the Neumann Laplacian, part 3Michael M. H. PangThis article is a sequel to two earlier articles (one of them written jointly with R. Banuelos) on stability results for the Neumann eigenvalues and eigenfunctions of domains in $mathbb{R}^2$ with a snowflake type fractal boundary. In particular we want our results to be applicable to the Koch snowflake domain. In the two earlier papers we assumed that a domain $Omegasubseteqmathbb{R}^2$ which has a snowflake type boundary is approximated by a family of subdomains and that the Neumann heat kernel of $Omega$ and those of its approximating subdomains satisfy a uniform bound for all sufficiently small t>0. The purpose of this paper is to extend the results in the two earlier papers to the situations where the approximating domains are not necessarily subdomains of $Omega$. We then apply our results to the Koch snowflake domain when it is approximated from outside by a decreasing sequence of polygons.http://ejde.math.txstate.edu/Volumes/2011/100/abstr.htmlStabilityapproximationsNeumann eigenvaluesand eigenfunctions |
| spellingShingle | Michael M. H. Pang Stability and approximations of eigenvalues and eigenfunctions of the Neumann Laplacian, part 3 Electronic Journal of Differential Equations Stability approximations Neumann eigenvalues and eigenfunctions |
| title | Stability and approximations of eigenvalues and eigenfunctions of the Neumann Laplacian, part 3 |
| title_full | Stability and approximations of eigenvalues and eigenfunctions of the Neumann Laplacian, part 3 |
| title_fullStr | Stability and approximations of eigenvalues and eigenfunctions of the Neumann Laplacian, part 3 |
| title_full_unstemmed | Stability and approximations of eigenvalues and eigenfunctions of the Neumann Laplacian, part 3 |
| title_short | Stability and approximations of eigenvalues and eigenfunctions of the Neumann Laplacian, part 3 |
| title_sort | stability and approximations of eigenvalues and eigenfunctions of the neumann laplacian part 3 |
| topic | Stability approximations Neumann eigenvalues and eigenfunctions |
| url | http://ejde.math.txstate.edu/Volumes/2011/100/abstr.html |
| work_keys_str_mv | AT michaelmhpang stabilityandapproximationsofeigenvaluesandeigenfunctionsoftheneumannlaplacianpart3 |