Bounds to eigenvalues of the Laplacian on L-shaped domain by variational methods

In this study, the bounds for eigenvalues of the Laplacian operator on an L-shaped domain are determined. By adopting some special functions in Goerisch method for lower bounds and in traditional Rayleigh–Ritz method for upper bounds, very accurate bounds to eigenvalues for the problem are obtained. Numerical results show that these functions can also be successfully used to solve the problem on the region with other reentrant angle.