The eigenvalues of the Laplacian on domains with small slits
We introduce a small slit into a planar domain and study the resulting effect upon the eigenvalues of the Laplacian. In particular, we show that as the length of the slit tends to zero, each real-analytic eigenvalue branch tends to an eigenvalue of the original domain. By combining this with our ear...
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| Veröffentlicht in: | Transactions of the American Mathematical Society 2010-12, Vol.362 (12), p.6231-6259 |
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| container_title | Transactions of the American Mathematical Society |
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| creator | Hillairet, Luc Judge, Chris |
| description | We introduce a small slit into a planar domain and study the resulting effect upon the eigenvalues of the Laplacian. In particular, we show that as the length of the slit tends to zero, each real-analytic eigenvalue branch tends to an eigenvalue of the original domain. By combining this with our earlier work (2009), we obtain the following application: The generic multiply connected polygon has a simple spectrum. |
| doi_str_mv | 10.1090/S0002-9947-2010-04943-8 |
| format | Article |
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By combining this with our earlier work (2009), we obtain the following application: The generic multiply connected polygon has a simple spectrum.</description><subject>Analysis of PDEs</subject><subject>Boundary conditions</subject><subject>Coordinate systems</subject><subject>Eigenfunctions</subject><subject>Eigenvalues</subject><subject>Exact sciences and technology</subject><subject>General mathematics</subject><subject>General, history and biography</subject><subject>Geometry</subject><subject>Laplacians</subject><subject>Mathematical theorems</subject><subject>Mathematics</subject><subject>Mathieu function</subject><subject>Nonlinear algebraic and transcendental equations</subject><subject>Numerical analysis</subject><subject>Numerical analysis. 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Scientific computation</topic><topic>Numerical linear algebra</topic><topic>Polygons</topic><topic>Research article</topic><topic>Sciences and techniques of general use</topic><topic>Spectral Theory</topic><topic>Vertices</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Hillairet, Luc</creatorcontrib><creatorcontrib>Judge, Chris</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Hyper Article en Ligne (HAL)</collection><jtitle>Transactions of the American Mathematical Society</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Hillairet, Luc</au><au>Judge, Chris</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The eigenvalues of the Laplacian on domains with small slits</atitle><jtitle>Transactions of the American Mathematical Society</jtitle><stitle>Trans. Amer. Math. 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| source | Jstor Complete Legacy; American Mathematical Society Publications; American Mathematical Society Publications (Freely Accessible); Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; JSTOR Mathematics & Statistics |
| subjects | Analysis of PDEs Boundary conditions Coordinate systems Eigenfunctions Eigenvalues Exact sciences and technology General mathematics General, history and biography Geometry Laplacians Mathematical theorems Mathematics Mathieu function Nonlinear algebraic and transcendental equations Numerical analysis Numerical analysis. Scientific computation Numerical linear algebra Polygons Research article Sciences and techniques of general use Spectral Theory Vertices |
| title | The eigenvalues of the Laplacian on domains with small slits |
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