Physical Sciences and Mathematics Commons^™

Convergence Of Eigenvalues For Elliptic Systems On Domains With Thin Tubes And The Green Function For The Mixed Problem, Justin L. Taylor

University of Kentucky Doctoral Dissertations

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 …