Spectral estimates of the p-Laplace Neumann operator and Brennan’s conjecture

@article{Goldshtein2017SpectralEO,
  title={Spectral estimates of the p-Laplace Neumann operator and Brennan’s conjecture},
  author={Vladimir Gol'dshtein and V. A. Pchelintsev and Alexander Ukhlov},
  journal={Bollettino dell'Unione Matematica Italiana},
  year={2017},
  volume={11},
  pages={245-264}
}
In this paper we obtain lower estimates for the first non-trivial eigenvalue of the p-Laplace Neumann operator in bounded simply connected planar domains $$\varOmega \subset {\mathbb {R}}^2$$Ω⊂R2. This study is based on a quasiconformal version of the universal two-weight Poincaré–Sobolev inequalities obtained in our previous papers for conformal weights and its non weighted version for so-called K-quasiconformal $$\alpha $$α-regular domains. The main technical tool is the geometric theory of… 

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