Approximation of Eigenvalues of Elliptic Operators with Discontinuous Coefficients
Shuichi Jimbo, Satoshi Kosugi · Communications in Partial Differential Equations · 2003
The asymptotic behavior of eigenvalues of an elliptic operator with a divergence form is discussed. The coefficients of the operator are discontinuous through a boundary of a subdomain and degenerate to zero on the subdomain when a parameter tends to zero. We will prove that the eigenvalues approach eigenvalues of the Laplacian on the subdomain or on the complement. We will obtain precise asymptotic behavior of their convergence.