Spectral Estimates of the p-Laplace Neumann operator and Brennan's Conjecture

2017/01/18 by Gol'dshtein, Vladimir, Pchelintsev, Valerii, Ukhlov, Alexander
#30C65 #35P15 #46E35 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1701.05143

Abstract

In this paper we obtain estimates for the first nontrivial eigenvalue of the p-Laplace Neumann operator in bounded simply connected planar domains Ω⊂\mathbb R². This study is based on a quasiconformal version of the universal weighted Poincaré-Sobolev inequalities obtained in our previous papers for conformal weights. The suggested weights in the present paper are Jacobians of quasiconformal mappings. The main technical tool is the theory of composition operators in relation with the Brennan's Conjecture for (quasi)conformal mappings.

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