TY - JOUR
AU1 - Gol’dshtein, Vladimir
AU2 - Pchelintsev, Valerii
AU3 - 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