Bounding Eigenvalues of Elliptic Operators
James R. Kuttler, Vincent G. Sigillito · SIAM Journal on Mathematical Analysis · 1978
We present a method which bounds the error between an estimate for a point in the spectrum and an eigenvalue of self-adjoint elliptic operators. The method makes use of trial functions which need not satisfy the boundary conditions of the problem. By using rough preliminary estimates for the eigenvalues this method gives both upper and lower bounds.