Inverse norm estimation of perturbed Laplace operators and corresponding eigenvalue problems
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The purpose of this paper is to reveal an eigenvalue problem corresponding to a perturbed Laplace operator -Δ - Q for a linear bounded operator Q on L^2(Ω). To verify the invertibility of the perturbed operator and explicitly evaluate its inverse norm, we evaluate the eigenvalues of the revealed problem based on Liu's approach with certain a priori error estimates. The accuracy is further improved using Lehman-Goerisch's method. The proposed method is applied to inverse norm estimation for a system of elliptic equations.
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