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

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6 Scopus citations


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.

Original languageEnglish
Pages (from-to)245-264
Number of pages20
JournalBolletino dell Unione Matematica Italiana
Issue number2
StatePublished - 1 Jun 2018


  • Elliptic equations
  • Quasiconformal mappings
  • Sobolev spaces

ASJC Scopus subject areas

  • Mathematics (all)


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