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Sharp Estimates for Eigenfunctions of a Neumann Problem

In this paper we provide some bounds for eigenfunctions of the Laplacian with homogeneous Neumann boundary conditions in a bounded domain Ω of ℝ n . To this aim we use the so-called symmetrization techniques and the obtained estimates are asymptotically sharp, at least in the bidimensional case, when the isoperimetric constant relative to Ω goes to 0.