I consider Dirichlet eigenvalues for an elliptic system in a region that consists of two domains joined by a thin tube. Under quite general conditions, I am able to give a rate on the convergence of the eigenvalues as the tube shrinks away. I make no assumption on the smoothness of the coefficients and only mild assumptions on the boundary of the domain.
Also, I consider the Green function associated with the mixed problem on a Lipschitz domain with a general decomposition of the boundary. I show that the Green function is Hölder continuous, which shows how a solution to the mixed problem behaves.
| Identifer | oai:union.ndltd.org:uky.edu/oai:uknowledge.uky.edu:gradschool_diss-1161 |
| Date | 01 January 2011 |
| Creators | Taylor, Justin L. |
| Publisher | UKnowledge |
| Source Sets | University of Kentucky |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | University of Kentucky Doctoral Dissertations |
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