For bounded pseudoconvex domains in C^n, the variational eigenvalues of the ∂-Neumann Laplacian are upper and lower semicontinuous under Hausdorff perturbation, with quantitative Lipschitz-type rates on uniformly finite D'Angelo type domains.
Straube , Global regularity for the -Neumann problem: a survey of the L^2 - S obolev theory , Several Complex Variables, MSRI Publications, vol
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Spectral Stability of the $\bar\partial-$Neumann Laplacian: Domain Perturbations
For bounded pseudoconvex domains in C^n, the variational eigenvalues of the ∂-Neumann Laplacian are upper and lower semicontinuous under Hausdorff perturbation, with quantitative Lipschitz-type rates on uniformly finite D'Angelo type domains.