Asymptotic solution of the Neumann problem in domains with thin bridges (Q1326036)

Let \(G_\varepsilon\subset \mathbb{R}^2\), the boundary of which near \((0, 0)\) is given by the equation \(x_2= x^{2\gamma}_1[F^+(x_1)+ \varepsilon]\) and \(x_2= x^{2\gamma}F^-(x_1)\), \(\gamma\) a natural number. The author announces asymptotic formulas of the Neumann problem as \(\varepsilon\to 0\). It should be remarked that the paper is written carelessly.