Composition Operators on Sobolev Spaces and Neumann Eigenvalues

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In this paper we discuss applications of the geometric theory of composition operators on Sobolev spaces to the spectral theory of non-linear elliptic operators. Lower estimates of the first non-trivial Neumann eigenvalues of the p-Laplace operator in cusp domains Ω ⊂ Rn, n≥ 2 , are given.

Original languageEnglish
Pages (from-to)2781-2798
Number of pages18
JournalComplex Analysis and Operator Theory
Issue number6
StatePublished - 1 Sep 2019


  • Neumann eigenvalues
  • Quasiconformal mappings
  • Sobolev spaces


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