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The first terms of the small volume asymptotic expansion for the splitting ofNeumann boundary condition Laplacian eigenvalues due to a grounded inclusion ofsize {\epsilon} are derived. An explicit formula to compute the first term fromthe eigenvalues and eigenfunctions of the unperturbed domain, the inclusionsize and position is given. As a consequence, when an eigenvalue of doublemultiplicity splits in two distinct eigenvalues, one decays likeO(1/log({\epsilon})), the other like O({\epsilon}^2).

Small volume expansion of the splitting of multiple Neumann Laplacian eigenvalues due to a grounded inclusion in two dimensions