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 A. 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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