Spectral estimates of the p-Laplace Neumann operator and Brennan's conjecture V. Gol'dshtein, V. A. Pchelintsev, A. Ukhlov
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ArticleSubject(s): эллиптические уравнения | Соболевские пространства | квазиконформные отображенияGenre/Form: статьи в журналах Online resources: Click here to access online
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Bollettino dell'Unione Matematica Italiana Vol. 11, № 2. P. 245-264Abstract: 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 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 α -regular domains. The main technical tool is the geometric theory of composition operators in relation with the Brennan’s conjecture for (quasi)conformal mappings.
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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 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 α -regular domains. The main technical tool is the geometric theory of composition operators in relation with the Brennan’s conjecture for (quasi)conformal mappings.
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