# Conformal spectral stability estimates for the Dirichlet Laplacian

@article{Burenkov2014ConformalSS, title={Conformal spectral stability estimates for the Dirichlet Laplacian}, author={Viktor I. Burenkov and V. A. Gol'dshtein and Alexander Ukhlov}, journal={Mathematische Nachrichten}, year={2014}, volume={288} }

We study the eigenvalue problem for the Dirichlet Laplacian in bounded simply connected plane domains Ω⊂C by reducing it, using conformal transformations, to the weighted eigenvalue problem for the Dirichlet Laplacian in the unit disc D . This allows us to estimate the variation of the eigenvalues of the Dirichlet Laplacian upon domain perturbation via energy type integrals for a large class of “conformal regular” domains which includes all quasidiscs, i.e. images of the unit disc under…

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