TY - JOUR AU - Ukhlov, Alexander AB - 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 ⊂ R 2 . 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 composition operators in relation with the Brennan’s conjecture for (quasi)conformal mappings. TI - Spectral estimates of the p-Laplace Neumann operator and Brennan’s conjecture JF - Bollettino dell Unione Matematica Italiana DO - 10.1007/s40574-017-0127-z DA - 2017-05-17 UR - https://www.deepdyve.com/lp/springer-journals/spectral-estimates-of-the-p-laplace-neumann-operator-and-brennan-s-IOym7USbjo SP - 245 EP - 264 VL - 11 IS - 2 DP - DeepDyve ER -