87 research outputs found
Spectral estimates of the -Laplace Neumann operator in conformal regular domains
In this paper we study spectral estimates of the -Laplace Neumann operator
in conformal regular domains . This study is based on
(weighted) Poincar\'e-Sobolev inequalities. The main technical tool is the
composition operators theory in relation with the Brennan's conjecture. We
prove that if the Brennan's conjecture holds then for any and
the weighted -Poincare-Sobolev inequality holds with
the constant depending on the conformal geometry of . As a consequence
we obtain classical Poincare-Sobolev inequalities and spectral estimates for
the first nontrivial eigenvalue of the -Laplace Neumann operator for
conformal regular domains.Comment: 15 page
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